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class="vector-toc-numb">1</span> <span>Eżempji</span> </div> </a> <ul id="toc-Eżempji-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definizzjoni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definizzjoni"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Definizzjoni</span> </div> </a> <button aria-controls="toc-Definizzjoni-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uri jew aħbi s-sottosezzjoni Definizzjoni</span> </button> <ul id="toc-Definizzjoni-sublist" class="vector-toc-list"> <li id="toc-Definizzjoni_alternattiva" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Definizzjoni_alternattiva"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Definizzjoni alternattiva</span> </div> </a> <ul id="toc-Definizzjoni_alternattiva-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Operazzjonijiet_fuq_il-funzjonijiet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Operazzjonijiet_fuq_il-funzjonijiet"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Operazzjonijiet fuq il-funzjonijiet</span> </div> </a> <ul id="toc-Operazzjonijiet_fuq_il-funzjonijiet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notazzjonijiet_għall-funzjonijiet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notazzjonijiet_għall-funzjonijiet"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notazzjonijiet għall-funzjonijiet</span> </div> </a> <button aria-controls="toc-Notazzjonijiet_għall-funzjonijiet-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uri jew aħbi s-sottosezzjoni Notazzjonijiet għall-funzjonijiet</span> </button> <ul id="toc-Notazzjonijiet_għall-funzjonijiet-sublist" class="vector-toc-list"> <li id="toc-Funzjonijiet_ta’_żewġ_varjabbli_jew_iżjed" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funzjonijiet_ta’_żewġ_varjabbli_jew_iżjed"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Funzjonijiet ta’ żewġ varjabbli jew iżjed</span> </div> </a> <ul id="toc-Funzjonijiet_ta’_żewġ_varjabbli_jew_iżjed-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Funzjonijiet_ta’_iżjed_valuri" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funzjonijiet_ta’_iżjed_valuri"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Funzjonijiet ta’ iżjed valuri</span> </div> </a> <ul id="toc-Funzjonijiet_ta’_iżjed_valuri-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Operazzjonijiet_binarji" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Operazzjonijiet_binarji"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Operazzjonijiet binarji</span> </div> </a> <ul id="toc-Operazzjonijiet_binarji-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Klassifikazzjoni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Klassifikazzjoni"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Klassifikazzjoni</span> </div> </a> <button aria-controls="toc-Klassifikazzjoni-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uri jew aħbi s-sottosezzjoni Klassifikazzjoni</span> </button> <ul id="toc-Klassifikazzjoni-sublist" class="vector-toc-list"> <li id="toc-Klassifikazzjoni_bbażata_purament_fuq_is-settijiet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Klassifikazzjoni_bbażata_purament_fuq_is-settijiet"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Klassifikazzjoni bbażata purament fuq is-settijiet</span> </div> </a> <ul id="toc-Klassifikazzjoni_bbażata_purament_fuq_is-settijiet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Klassifikazzjoni_bbażata_fuq_it-tip_ta’_dominju_u_kodominju" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Klassifikazzjoni_bbażata_fuq_it-tip_ta’_dominju_u_kodominju"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Klassifikazzjoni bbażata fuq it-tip ta’ dominju u kodominju</span> </div> </a> <ul id="toc-Klassifikazzjoni_bbażata_fuq_it-tip_ta’_dominju_u_kodominju-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Klassifikazzjoni_tal-funzjonijiet_mill-ambitu_tal-kalkulabbilià" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Klassifikazzjoni_tal-funzjonijiet_mill-ambitu_tal-kalkulabbilià"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Klassifikazzjoni tal-funzjonijiet mill-ambitu tal-kalkulabbilià</span> </div> </a> <ul id="toc-Klassifikazzjoni_tal-funzjonijiet_mill-ambitu_tal-kalkulabbilià-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Klassifikazzjoni_tal-funzjonijiet_ta’_l-analisi_infiniteżmali" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Klassifikazzjoni_tal-funzjonijiet_ta’_l-analisi_infiniteżmali"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Klassifikazzjoni tal-funzjonijiet ta’ l-analisi infiniteżmali</span> </div> </a> <ul id="toc-Klassifikazzjoni_tal-funzjonijiet_ta’_l-analisi_infiniteżmali-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xi_funzjonijiet_magħrufa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xi_funzjonijiet_magħrufa"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Xi funzjonijiet magħrufa</span> </div> </a> <ul id="toc-Xi_funzjonijiet_magħrufa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Funzjonijiet_ta’_interess_probabilistiku_u_statistiku" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Funzjonijiet_ta’_interess_probabilistiku_u_statistiku"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Funzjonijiet ta’ interess probabilistiku u statistiku</span> </div> </a> <ul id="toc-Funzjonijiet_ta’_interess_probabilistiku_u_statistiku-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Kontenut" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Aħbi jew uri l-werrej" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Aħbi jew uri l-werrej</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Funzjonijiet (matematika)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Żur artiklu f'lingwa differenti. Disponibbli fi 120 lingwi" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-120" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">120 lingwi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Funksie" title="Funksie – Afrikans" lang="af" hreflang="af" data-title="Funksie" data-language-autonym="Afrikaans" data-language-local-name="Afrikans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Funktion_(Mathematik)" title="Funktion (Mathematik) – Ġermaniż tal-Iżvizzera" lang="gsw" hreflang="gsw" data-title="Funktion (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="Ġermaniż tal-Iżvizzera" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%B5%E1%88%A8%E1%8A%AB%E1%89%A2" title="አስረካቢ – Amhariku" lang="am" hreflang="am" data-title="አስረካቢ" data-language-autonym="አማርኛ" data-language-local-name="Amhariku" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Funci%C3%B3n_matematica" title="Función matematica – Aragoniż" lang="an" hreflang="an" data-title="Función matematica" data-language-autonym="Aragonés" data-language-local-name="Aragoniż" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9" title="دالة – Għarbi" lang="ar" hreflang="ar" data-title="دالة" data-language-autonym="العربية" data-language-local-name="Għarbi" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%AF%D8%A7%D9%84%D8%A9" title="دالة – Moroccan Arabic" lang="ary" hreflang="ary" data-title="دالة" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Funci%C3%B3n_matem%C3%A1tica" title="Función matemática – Asturian" lang="ast" hreflang="ast" data-title="Función matemática" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Funksiya_(riyaziyyat)" title="Funksiya (riyaziyyat) – Ażerbajġani" lang="az" hreflang="az" data-title="Funksiya (riyaziyyat)" data-language-autonym="Azərbaycanca" data-language-local-name="Ażerbajġani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – Bashkir" lang="ba" hreflang="ba" data-title="Функция (математика)" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Funkc%C4%97j%C4%97" title="Funkcėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Funkcėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Функцыя (матэматыка) – Belarussu" lang="be" hreflang="be" data-title="Функцыя (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="Belarussu" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Функцыя (матэматыка) – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Функцыя (матэматыка)" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Функция – Bulgaru" lang="bg" hreflang="bg" data-title="Функция" data-language-autonym="Български" data-language-local-name="Bulgaru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AB%E0%A4%82%E0%A4%95%E0%A5%8D%E0%A4%B6%E0%A4%A8_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="फंक्शन (गणित) – Bhojpuri" lang="bh" hreflang="bh" data-title="फंक्शन (गणित)" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%95_(%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4)" title="অপেক্ষক (গণিত) – Bengali" lang="bn" hreflang="bn" data-title="অপেক্ষক (গণিত)" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – Bożnijaku" lang="bs" hreflang="bs" data-title="Funkcija (matematika)" data-language-autonym="Bosanski" data-language-local-name="Bożnijaku" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Funci%C3%B3" title="Funció – Katalan" lang="ca" hreflang="ca" data-title="Funció" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%81%D8%A7%D9%86%DA%A9%D8%B4%D9%86_(%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9)" title="فانکشن (ماتماتیک) – Kurd Ċentrali" lang="ckb" hreflang="ckb" data-title="فانکشن (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="Kurd Ċentrali" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Funkce_(matematika)" title="Funkce (matematika) – Ċek" lang="cs" hreflang="cs" data-title="Funkce (matematika)" data-language-autonym="Čeština" data-language-local-name="Ċek" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функци (математика) – Chuvash" lang="cv" hreflang="cv" data-title="Функци (математика)" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ffwythiant" title="Ffwythiant – Welsh" lang="cy" hreflang="cy" data-title="Ffwythiant" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Funktion_(matematik)" title="Funktion (matematik) – Daniż" lang="da" hreflang="da" data-title="Funktion (matematik)" data-language-autonym="Dansk" data-language-local-name="Daniż" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Funktion_(Mathematik)" title="Funktion (Mathematik) – Ġermaniż" lang="de" hreflang="de" data-title="Funktion (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="Ġermaniż" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7" title="Συνάρτηση – Grieg" lang="el" hreflang="el" data-title="Συνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="Grieg" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – Ingliż" lang="en" hreflang="en" data-title="Function (mathematics)" data-language-autonym="English" data-language-local-name="Ingliż" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Funkcio_(matematiko)" title="Funkcio (matematiko) – Esperanto" lang="eo" hreflang="eo" data-title="Funkcio (matematiko)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Funci%C3%B3n_(matem%C3%A1tica)" title="Función (matemática) – Spanjol" lang="es" hreflang="es" data-title="Función (matemática)" data-language-autonym="Español" data-language-local-name="Spanjol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Funktsioon_(matemaatika)" title="Funktsioon (matemaatika) – Estonjan" lang="et" hreflang="et" data-title="Funktsioon (matemaatika)" data-language-autonym="Eesti" data-language-local-name="Estonjan" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Funtzio_(matematika)" title="Funtzio (matematika) – Bask" lang="eu" hreflang="eu" data-title="Funtzio (matematika)" data-language-autonym="Euskara" data-language-local-name="Bask" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%A8%D8%B9" title="تابع – Persjan" lang="fa" hreflang="fa" data-title="تابع" data-language-autonym="فارسی" data-language-local-name="Persjan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Funktio" title="Funktio – Finlandiż" lang="fi" hreflang="fi" data-title="Funktio" data-language-autonym="Suomi" data-language-local-name="Finlandiż" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Cakacaka_(fika)" title="Cakacaka (fika) – Fiġjan" lang="fj" hreflang="fj" data-title="Cakacaka (fika)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fiġjan" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Funksj%C3%B3n" title="Funksjón – Faroese" lang="fo" hreflang="fo" data-title="Funksjón" data-language-autonym="Føroyskt" data-language-local-name="Faroese" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fonction_(math%C3%A9matiques)" title="Fonction (mathématiques) – Franċiż" lang="fr" hreflang="fr" data-title="Fonction (mathématiques)" data-language-autonym="Français" data-language-local-name="Franċiż" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Funksion" title="Funksion – Northern Frisian" lang="frr" hreflang="frr" data-title="Funksion" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Feidhm_(matamaitic)" title="Feidhm (matamaitic) – Irlandiż" lang="ga" hreflang="ga" data-title="Feidhm (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="Irlandiż" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%87%BD%E6%95%B8" title="函數 – Gan" lang="gan" hreflang="gan" data-title="函數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Fonksyon_(mat%C3%A9matik)" title="Fonksyon (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Fonksyon (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Funci%C3%B3n" title="Función – Galiċjan" lang="gl" hreflang="gl" data-title="Función" data-language-autonym="Galego" data-language-local-name="Galiċjan" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94" title="פונקציה – Ebrajk" lang="he" hreflang="he" data-title="פונקציה" data-language-autonym="עברית" data-language-local-name="Ebrajk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="फलन – Hindi" lang="hi" hreflang="hi" data-title="फलन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Function" title="Function – Fiji Hindi" lang="hif" hreflang="hif" data-title="Function" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – Kroat" lang="hr" hreflang="hr" data-title="Funkcija (matematika)" data-language-autonym="Hrvatski" data-language-local-name="Kroat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%BCggv%C3%A9ny_(matematika)" title="Függvény (matematika) – Ungeriż" lang="hu" hreflang="hu" data-title="Függvény (matematika)" data-language-autonym="Magyar" data-language-local-name="Ungeriż" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Ֆունկցիա (մաթեմատիկա) – Armen" lang="hy" hreflang="hy" data-title="Ֆունկցիա (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armen" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Function_(mathematica)" title="Function (mathematica) – Interlingua" lang="ia" hreflang="ia" data-title="Function (mathematica)" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_(matematika)" title="Fungsi (matematika) – Indoneżjan" lang="id" hreflang="id" data-title="Fungsi (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indoneżjan" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Funciono" title="Funciono – Ido" lang="io" hreflang="io" data-title="Funciono" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fall_(st%C3%A6r%C3%B0fr%C3%A6%C3%B0i)" title="Fall (stærðfræði) – Iżlandiż" lang="is" hreflang="is" data-title="Fall (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="Iżlandiż" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Funzione_(matematica)" title="Funzione (matematica) – Taljan" lang="it" hreflang="it" data-title="Funzione (matematica)" data-language-autonym="Italiano" data-language-local-name="Taljan" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%96%A2%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="関数 (数学) – Ġappuniż" lang="ja" hreflang="ja" data-title="関数 (数学)" data-language-autonym="日本語" data-language-local-name="Ġappuniż" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Fongshan_(matimatix)" title="Fongshan (matimatix) – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Fongshan (matimatix)" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/fancu" title="fancu – Lojban" lang="jbo" hreflang="jbo" data-title="fancu" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A4%E1%83%A3%E1%83%9C%E1%83%A5%E1%83%AA%E1%83%98%E1%83%90_(%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90)" title="ფუნქცია (მათემატიკა) – Ġorġjan" lang="ka" hreflang="ka" data-title="ფუნქცია (მათემატიკა)" data-language-autonym="ქართული" data-language-local-name="Ġorġjan" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tas%C9%A3ent_(tusnakt)" title="Tasɣent (tusnakt) – Kabuljan" lang="kab" hreflang="kab" data-title="Tasɣent (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="Kabuljan" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/K%C9%A9lab%C9%A9m" title="Kɩlabɩm – Kabiye" lang="kbp" hreflang="kbp" data-title="Kɩlabɩm" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – Każak" lang="kk" hreflang="kk" data-title="Функция (математика)" data-language-autonym="Қазақша" data-language-local-name="Każak" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%A8%EC%88%98" title="함수 – Korean" lang="ko" hreflang="ko" data-title="함수" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Functio" title="Functio – Latin" lang="la" hreflang="la" data-title="Functio" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Funktioun_(Mathematik)" title="Funktioun (Mathematik) – Lussemburgiż" lang="lb" hreflang="lb" data-title="Funktioun (Mathematik)" data-language-autonym="Lëtzebuergesch" data-language-local-name="Lussemburgiż" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fonzion_(matematega)" title="Fonzion (matematega) – Lombard" lang="lmo" hreflang="lmo" data-title="Fonzion (matematega)" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%95%E0%BA%B3%E0%BA%A5%E0%BA%B2_(%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94)" title="ຕຳລາ (ຄະນິດສາດ) – Laosjan" lang="lo" hreflang="lo" data-title="ຕຳລາ (ຄະນິດສາດ)" data-language-autonym="ລາວ" data-language-local-name="Laosjan" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – Litwan" lang="lt" hreflang="lt" data-title="Funkcija (matematika)" data-language-autonym="Lietuvių" data-language-local-name="Litwan" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Funkcija" title="Funkcija – Latvjan" lang="lv" hreflang="lv" data-title="Funkcija" data-language-autonym="Latviešu" data-language-local-name="Latvjan" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функција (математика) – Maċedonjan" lang="mk" hreflang="mk" data-title="Функција (математика)" data-language-autonym="Македонски" data-language-local-name="Maċedonjan" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B4%99%E0%B5%8D%E0%B4%B7%E0%B5%BB" title="ഫങ്ഷൻ – Malayalam" lang="ml" hreflang="ml" data-title="ഫങ്ഷൻ" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)" title="Функц (математик) – Mongoljan" lang="mn" hreflang="mn" data-title="Функц (математик)" data-language-autonym="Монгол" data-language-local-name="Mongoljan" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AB%E0%A4%B2_(%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="फल (गणित) – Marathi" lang="mr" hreflang="mr" data-title="फल (गणित)" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Fungsi" title="Fungsi – Malay" lang="ms" hreflang="ms" data-title="Fungsi" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%96%E1%80%94%E1%80%BA%E1%80%9B%E1%80%BE%E1%80%84%E1%80%BA" title="ဖန်ရှင် – Burmiż" lang="my" hreflang="my" data-title="ဖန်ရှင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmiż" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Afbillen_(Mathematik)" title="Afbillen (Mathematik) – Ġermaniż Komuni" lang="nds" hreflang="nds" data-title="Afbillen (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="Ġermaniż Komuni" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Functie_(wiskunde)" title="Functie (wiskunde) – Olandiż" lang="nl" hreflang="nl" data-title="Functie (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="Olandiż" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Matematisk_funksjon" title="Matematisk funksjon – Ninorsk Norveġiż" lang="nn" hreflang="nn" data-title="Matematisk funksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Ninorsk Norveġiż" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Funksjon_(matematikk)" title="Funksjon (matematikk) – Bokmal Norveġiż" lang="nb" hreflang="nb" data-title="Funksjon (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmal Norveġiż" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Aplicacion_(matematicas)" title="Aplicacion (matematicas) – Oċċitan" lang="oc" hreflang="oc" data-title="Aplicacion (matematicas)" data-language-autonym="Occitan" data-language-local-name="Oċċitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Warroomii_(faankishinii)" title="Warroomii (faankishinii) – Oromo" lang="om" hreflang="om" data-title="Warroomii (faankishinii)" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AB%E0%A9%B0%E0%A8%95%E0%A8%B8%E0%A8%BC%E0%A8%A8_(%E0%A8%B9%E0%A8%BF%E0%A8%B8%E0%A8%BE%E0%A8%AC)" title="ਫੰਕਸ਼ਨ (ਹਿਸਾਬ) – Punjabi" lang="pa" hreflang="pa" data-title="ਫੰਕਸ਼ਨ (ਹਿਸਾਬ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funkcja" title="Funkcja – Pollakk" lang="pl" hreflang="pl" data-title="Funkcja" data-language-autonym="Polski" data-language-local-name="Pollakk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Fonsion" title="Fonsion – Piedmontese" lang="pms" hreflang="pms" data-title="Fonsion" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%81%D9%86%DA%A9%D8%B4%D9%86" title="فنکشن – Western Punjabi" lang="pnb" hreflang="pnb" data-title="فنکشن" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_(matem%C3%A1tica)" title="Função (matemática) – Portugiż" lang="pt" hreflang="pt" data-title="Função (matemática)" data-language-autonym="Português" data-language-local-name="Portugiż" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Kinraysuyu" title="Kinraysuyu – Quechua" lang="qu" hreflang="qu" data-title="Kinraysuyu" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Func%C8%9Bie" title="Funcție – Rumen" lang="ro" hreflang="ro" data-title="Funcție" data-language-autonym="Română" data-language-local-name="Rumen" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – Russu" lang="ru" hreflang="ru" data-title="Функция (математика)" data-language-autonym="Русский" data-language-local-name="Russu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F._%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_%D1%87%D1%8D%D1%80%D1%87%D0%B8%D1%82%D1%8D,_%D1%81%D1%83%D0%BE%D0%BB%D1%82%D0%B0%D0%BB%D0%B0%D1%80%D1%8B%D0%BD_%D1%82%D2%AF%D0%BC%D1%81%D1%8D%D1%8D%D0%BD%D1%8D" title="Функция. Функция чэрчитэ, суолталарын түмсээнэ – Sakha" lang="sah" hreflang="sah" data-title="Функция. Функция чэрчитэ, суолталарын түмсээнэ" data-language-autonym="Саха тыла" data-language-local-name="Sakha" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Funzioni_(matim%C3%A0tica)" title="Funzioni (matimàtica) – Sqalli" lang="scn" hreflang="scn" data-title="Funzioni (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="Sqalli" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – Skoċċiż" lang="sco" hreflang="sco" data-title="Function (mathematics)" data-language-autonym="Scots" data-language-local-name="Skoċċiż" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Funkcija" title="Funkcija – Serbo-Kroat" lang="sh" hreflang="sh" data-title="Funkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Function_(mathematics)" title="Function (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Function (mathematics)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Zobrazenie_(matematika)" title="Zobrazenie (matematika) – Slovakk" lang="sk" hreflang="sk" data-title="Zobrazenie (matematika)" data-language-autonym="Slovenčina" data-language-local-name="Slovakk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Funkcija_(matematika)" title="Funkcija (matematika) – Sloven" lang="sl" hreflang="sl" data-title="Funkcija (matematika)" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Funktio" title="Funktio – Inari Sami" lang="smn" hreflang="smn" data-title="Funktio" data-language-autonym="Anarâškielâ" data-language-local-name="Inari Sami" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Murimo_(Masvomhu)" title="Murimo (Masvomhu) – Shona" lang="sn" hreflang="sn" data-title="Murimo (Masvomhu)" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Shaqada_(xisaabta)" title="Shaqada (xisaabta) – Somali" lang="so" hreflang="so" data-title="Shaqada (xisaabta)" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Funksioni" title="Funksioni – Albaniż" lang="sq" hreflang="sq" data-title="Funksioni" data-language-autonym="Shqip" data-language-local-name="Albaniż" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функција (математика) – Serb" lang="sr" hreflang="sr" data-title="Функција (математика)" data-language-autonym="Српски / srpski" data-language-local-name="Serb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Fungsi_(matematika)" title="Fungsi (matematika) – Sundaniż" lang="su" hreflang="su" data-title="Fungsi (matematika)" data-language-autonym="Sunda" data-language-local-name="Sundaniż" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Funktion" title="Funktion – Żvediż" lang="sv" hreflang="sv" data-title="Funktion" data-language-autonym="Svenska" data-language-local-name="Żvediż" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Funkcyjo" title="Funkcyjo – Silesian" lang="szl" hreflang="szl" data-title="Funkcyjo" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81" title="சார்பு – Tamil" lang="ta" hreflang="ta" data-title="சார்பு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9F%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B9%8C%E0%B8%8A%E0%B8%B1%E0%B8%99_(%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="ฟังก์ชัน (คณิตศาสตร์) – Tajlandiż" lang="th" hreflang="th" data-title="ฟังก์ชัน (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="Tajlandiż" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Punsiyon_(matematika)" title="Punsiyon (matematika) – Tagalog" lang="tl" hreflang="tl" data-title="Punsiyon (matematika)" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Fonksiyon" title="Fonksiyon – Tork" lang="tr" hreflang="tr" data-title="Fonksiyon" data-language-autonym="Türkçe" data-language-local-name="Tork" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – Tatar" lang="tt" hreflang="tt" data-title="Функция (математика)" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функция (математика) – Udmurt" lang="udm" hreflang="udm" data-title="Функция (математика)" data-language-autonym="Удмурт" data-language-local-name="Udmurt" class="interlanguage-link-target"><span>Удмурт</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D9%81%DB%87%D9%86%D9%83%D8%B3%D9%89%D9%8A%DB%95" title="فۇنكسىيە – Uyghur" lang="ug" hreflang="ug" data-title="فۇنكسىيە" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Функція (математика) – Ukren" lang="uk" hreflang="uk" data-title="Функція (математика)" data-language-autonym="Українська" data-language-local-name="Ukren" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B9%D9%84_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="تفاعل (ریاضیات) – Urdu" lang="ur" hreflang="ur" data-title="تفاعل (ریاضیات)" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Funksiya_(matematika)" title="Funksiya (matematika) – Uzbek" lang="uz" hreflang="uz" data-title="Funksiya (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Funkcii_(matematik)" title="Funkcii (matematik) – Veps" lang="vep" hreflang="vep" data-title="Funkcii (matematik)" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%A0m_s%E1%BB%91" title="Hàm số – Vjetnamiż" lang="vi" hreflang="vi" data-title="Hàm số" data-language-autonym="Tiếng Việt" data-language-local-name="Vjetnamiż" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Funsiyon_(matematika)" title="Funsiyon (matematika) – Waray" lang="war" hreflang="war" data-title="Funsiyon (matematika)" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%87%BD%E6%95%B0" title="函数 – Wu" lang="wuu" hreflang="wuu" data-title="函数" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Функция – Kalmyk" lang="xal" hreflang="xal" data-title="Функция" data-language-autonym="Хальмг" data-language-local-name="Kalmyk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%A2" title="פונקציע – Yiddish" lang="yi" hreflang="yi" data-title="פונקציע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%99%E2%B5%96%E2%B5%8F%E2%B5%9C_(%E2%B5%9C%E2%B5%93%E2%B5%99%E2%B5%8F%E2%B4%B0%E2%B4%BD%E2%B5%9C)" title="ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ) – Tamazight Standard tal-Marokk" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ)" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Tamazight Standard tal-Marokk" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%BD%E6%95%B0" title="函数 – Ċiniż" lang="zh" hreflang="zh" data-title="函数" data-language-autonym="中文" data-language-local-name="Ċiniż" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical 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class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Dehra</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">aħbi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Minn Wikipedija, l-enċiklopedija l-ħielsa</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mt" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File"><a href="/wiki/Stampa:Funzjoni.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/mt/a/a7/Funzjoni.jpg" decoding="async" width="378" height="317" class="mw-file-element" data-file-width="378" data-file-height="317" /></a><figcaption></figcaption></figure> <p>Fil-<a href="/wiki/Matematika" title="Matematika">matematika</a>, <b>funzjoni</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> minn <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> għal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> hi magħmula minn: </p><p>1) <a href="/w/index.php?title=Sett&action=edit&redlink=1" class="new" title="Sett (il-paġna ma teżistix)">sett</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> imsejjaħ id-<b><a href="/w/index.php?title=Dominju_(matematika)&action=edit&redlink=1" class="new" title="Dominju (matematika) (il-paġna ma teżistix)">dominju</a></b> ta' <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> </p><p>2) sett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> imsejjaħ il-<b><a href="/w/index.php?title=Kodominju&action=edit&redlink=1" class="new" title="Kodominju (il-paġna ma teżistix)">kodominju</a></b> ta’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> </p><p>3) <b>liġi</b> li ma' kull element <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> f' <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> tassoċja element wieħed u wieħed biss <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69df108372019d93cfdc04fabe9dbb4cd67e4d59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.998ex; height:2.843ex;" alt="{\displaystyle \ f(x)}"></span> f' <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span>. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> jissejjaħ l-<b>argument</b> tal-funzjoni, jew inkella il-<b><a href="/wiki/Varjabbli" title="Varjabbli">varjabbli</a> indipendenti</b>, waqt li <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69df108372019d93cfdc04fabe9dbb4cd67e4d59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.998ex; height:2.843ex;" alt="{\displaystyle \ f(x)}"></span> huwa l-<b>valur</b> tal-funzjoni, jew inkella l-<b>varjabbli dipendenti</b>. </p><p>Dawn li ġejjin huma kliem sinonimi ma' "funzjoni": <br /> "<b>applikazzjoni</b>", "<b>operatur</b>", "<b>mappa</b>", "<b>relazzjoni binarja univoka</b>", "<b>trasformazzjoni</b>". </p><p>Dan il-kunċett hu fundamentali fil-friegħi kollha tal-matematika. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Eżempji"><span id="E.C5.BCempji"></span>Eżempji</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=1" title="Editja s-sezzjoni: Eżempji" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=1" title="Edit section's source code: Eżempji"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-iżjed eżempji sempliċi ta’ funzjonijiet huma dawk li bħala d-dominju u l-kodominju għandhom settijiet numeriċi. Pereżempju, jekk ma’ kull numru nassoċjaw id-doppju ta’ dak in-numru, ikollna funzjoni. Ma dan kollu nitkellmu fuq funzjoni anki meta d-dominju u l-kodominju jew it-tnejn ma jkunux settijiet ta’ numri. Pereżempju, jekk ma’ kull trianglu nassoċjaw iċ-ċirku inskritt fih, ikollna funzjoni għaliex għal kull trianglu jeżisti ċirku wieħed u wieħed biss li hu inskritt fih. </p><p>Sikwit nitkellmu fuq funzjonijet b’iżjed argumenti, jew b’iżjed valuri, pereżempju, funzjoni li l-koordinati <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x,y,z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x,y,z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5644d5dae21a88985f1b72458c9e021cbcd15de0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.222ex; height:2.009ex;" alt="{\displaystyle \ x,y,z}"></span> ta’ punt fl-ispazju torbothom mat-temperatura <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/630996e0f4ea15c1347439ec69ac78fc5ae2f755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.217ex; height:2.176ex;" alt="{\displaystyle \ T}"></span> u l-pressjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> ta’ l-arja. F’dan il-każ , il-funzjoni fir-realtà xorta għandha argument wieħed biss, li hu t-terna <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb9d98e83d71ef958a1bfbff62b8b3698fc017a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.031ex; height:2.843ex;" alt="{\displaystyle \ (x,y,z)}"></span> , u xorta għandha valur wieħed biss, li hu l-koppja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (T,P)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (T,P)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b54af9e6972e202b054e1ccd5e4b5ee65a995df0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.806ex; height:2.843ex;" alt="{\displaystyle \ (T,P)}"></span> . </p> <div class="mw-heading mw-heading2"><h2 id="Definizzjoni">Definizzjoni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=2" title="Editja s-sezzjoni: Definizzjoni" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=2" title="Edit section's source code: Definizzjoni"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mogħtija s-settijiet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span>, <a href="/w/index.php?title=Sottosett&action=edit&redlink=1" class="new" title="Sottosett (il-paġna ma teżistix)">sottosett</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> tal-<a href="/w/index.php?title=Prodott_Carte%C5%BCjan&action=edit&redlink=1" class="new" title="Prodott Carteżjan (il-paġna ma teżistix)">prodott Carteżjan</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X\times Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> <mo>×</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X\times Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4ec95e33d16d4aba38e69d4ccb7dadfe3a28ade" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.174ex; height:2.176ex;" alt="{\displaystyle \ X\times Y}"></span> insejħulu <b>funzjoni</b> minn <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> għal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span>, jekk għal kull <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x\in X\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> <mo>∈</mo> <mi>X</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x\in X\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a570b8983d915238f6147f73a21ba549994f8255" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.376ex; height:2.176ex;" alt="{\displaystyle \ x\in X\;}"></span>, jeżisti element wieħed u wieħed biss <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y\in Y\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> <mo>∈</mo> <mi>Y</mi> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y\in Y\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bdcd8f8cccf4b59e7311558d9b183e92f8313b84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.995ex; height:2.509ex;" alt="{\displaystyle \ y\in Y\;}"></span> tali <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (x,y)\in f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y)\in f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e68307f1e217fb847e15e832fe20f230b9fddaed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.028ex; height:2.843ex;" alt="{\displaystyle \ (x,y)\in f}"></span>. Dan l-element tradizzjonalment niddenotawh b’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69df108372019d93cfdc04fabe9dbb4cd67e4d59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.998ex; height:2.843ex;" alt="{\displaystyle \ f(x)}"></span>: fi kliem ieħor, minflok niktbu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (x,y)\in f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y)\in f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e68307f1e217fb847e15e832fe20f230b9fddaed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.028ex; height:2.843ex;" alt="{\displaystyle \ (x,y)\in f}"></span> nistgħu nużaw il-<i>kitba tradizzjonali</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y=f(x)\;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y=f(x)\;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a906a9e02a664ef2c04d7f6e5ab473fbd960c29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.897ex; height:2.843ex;" alt="{\displaystyle \ y=f(x)\;}"></span>. </p><p>Il-fatt li <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> hija funzjoni minn <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> għal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> li tassoċja ma’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> l-element <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69df108372019d93cfdc04fabe9dbb4cd67e4d59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.998ex; height:2.843ex;" alt="{\displaystyle \ f(x)}"></span> nistgħu nuruh billi niktbu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}f:&X&\rightarrow &Y\\&x&\mapsto &f(x)\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>f</mi> <mo>:</mo> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mo stretchy="false">→</mo> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>x</mi> </mtd> <mtd> <mo stretchy="false">↦</mo> </mtd> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}f:&X&\rightarrow &Y\\&x&\mapsto &f(x)\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4273179bd2fbb2d70d0d38b3498ec5a71fce1623" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:19.011ex; height:6.176ex;" alt="{\displaystyle {\begin{matrix}f:&X&\rightarrow &Y\\&x&\mapsto &f(x)\end{matrix}}}"></span></dd></dl> <p>Is-sett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> (li minnu l-funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> "tieħu" il-valuri) hu id-<b>dominju</b> tal-funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span>, waqt li s-sett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> (li fih insibu l-valuri "mogħtijin" mill-funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span>) hu l-<b>kodomiju</b> tal-funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span>. </p><p>Nosservaw li t-termini metaforiċi "tieħu valur" u "tagħti valur" jirreferu għal mudell mekkaniku tal-funzjonijiet li jirrapreżenthom bħala magna li meta ttiha element tad-dominju, <i>tittrasformah</i> fl-element imqabbel tal-kodominju. Minn din ix-xbieha jiġi s-sinonimu <i>trasformazzjoni</i>. </p><p>Is-sett </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{y\in Y|\exists x\in X|y=f(x)\},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>y</mi> <mo>∈</mo> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo>∈</mo> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{y\in Y|\exists x\in X|y=f(x)\},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b9e1c9a11bb29b381d0ba41272894f87708ab19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.149ex; height:2.843ex;" alt="{\displaystyle \{y\in Y|\exists x\in X|y=f(x)\},}"></span></dd></dl> <p>mogħti mill-elementi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64598c4f945fe21fbf547a5d349969c7e6d852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.736ex; height:2.009ex;" alt="{\displaystyle \ y}"></span> tal-kodominju li għalihom jeżisti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> fid-dominju li tittrasfoma f’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e64598c4f945fe21fbf547a5d349969c7e6d852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.736ex; height:2.009ex;" alt="{\displaystyle \ y}"></span> ngħidulu l-<b>immaġini</b> ta’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> u niddenotawh b’ Im<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,(f)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,(f)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a3a759761041797a5e9302750fe7cd46dcd17c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.475ex; height:2.843ex;" alt="{\displaystyle \,(f)}"></span> jew b’abbuż żgħir tal-lingwa b' <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d82d89649716a2cf393af377a66bb846cc8c17ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.649ex; height:2.843ex;" alt="{\displaystyle \ f(X)}"></span>. </p><p>Anki din it-termini ġejja minn mudell li jħares lejn funzjoni bħala sistema tad-dawl, pereżempju lenti; f’dal-mudell l-elementi tad-dominju jikkorrespondu ma’ ġħejun ta’ raġġi tad-dawl u l-elementi tal-kodominju ma’ fejn jolqtu r-raġġi jew l-immaġini. </p> <div class="mw-heading mw-heading3"><h3 id="Definizzjoni_alternattiva">Definizzjoni alternattiva</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=3" title="Editja s-sezzjoni: Definizzjoni alternattiva" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=3" title="Edit section's source code: Definizzjoni alternattiva"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Xi matematiċi jippreferixxu d-definizzjoni alternattiva ta’ funzjoni li ġejja, li għalkemm hi iżjed rigoruża, rari tintuża: </p> <dl><dd>Funzjoni hija terna ordnata <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (A,B,f)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (A,B,f)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e33e3a4a7de6f60c4a7cf5a10fd3a7755bbe2099" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.244ex; height:2.843ex;" alt="{\displaystyle \ (A,B,f)}"></span>, fejn <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a29b7d7604962065930f413ee72574d1f7a6e81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle \ A}"></span> hu sett, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c058f124591f21f86504adf1f4685023b3cf5518" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.345ex; height:2.176ex;" alt="{\displaystyle \ B}"></span> hu sett ieħor, u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f\subseteq A\times B\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo>⊆</mo> <mi>A</mi> <mo>×</mo> <mi>B</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f\subseteq A\times B\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61ca1e93c7c7fb442b90cb82ab1a33cec7db21b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.886ex; height:2.509ex;" alt="{\displaystyle \ f\subseteq A\times B\ }"></span> hu tali <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \forall a\in A\;\ \exists {\text{!}}b\in B\ |\ (a,b)\in f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>A</mi> <mspace width="thickmathspace" /> <mtext> </mtext> <mi mathvariant="normal">∃</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>!</mtext> </mrow> <mi>b</mi> <mo>∈</mo> <mi>B</mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \forall a\in A\;\ \exists {\text{!}}b\in B\ |\ (a,b)\in f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c3789d8383a91f5e43e76aaf86bb7301f3a90ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.452ex; height:2.843ex;" alt="{\displaystyle \ \forall a\in A\;\ \exists {\text{!}}b\in B\ |\ (a,b)\in f}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Operazzjonijiet_fuq_il-funzjonijiet">Operazzjonijiet fuq il-funzjonijiet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=4" title="Editja s-sezzjoni: Operazzjonijiet fuq il-funzjonijiet" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=4" title="Edit section's source code: Operazzjonijiet fuq il-funzjonijiet"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jekk ikollna żewġ funzjonijiet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> → <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c9d93a460e6e6f85291c2df324622a50eb75661" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.697ex; height:2.009ex;" alt="{\displaystyle \ g}"></span> : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5333f51b8fbff7ee7dcece248fc723549a85f5d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.354ex; height:2.009ex;" alt="{\displaystyle \ Y}"></span> → <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d9105e5f109f710fb6bf1d679c758202158aae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.261ex; height:2.176ex;" alt="{\displaystyle \ Z}"></span> nistgħu niddefinixxu l-<b><a href="/w/index.php?title=Kompo%C5%BCizzjoni&action=edit&redlink=1" class="new" title="Kompożizzjoni (il-paġna ma teżistix)">kompożizzjoni</a></b> tagħhom: din hi definita bħala l-applikazzjoni l-ewwel ta’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> fuq <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span> u mbagħad l-applikazzjoni ta’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c9d93a460e6e6f85291c2df324622a50eb75661" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.697ex; height:2.009ex;" alt="{\displaystyle \ g}"></span> fuq ir-riżultat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69df108372019d93cfdc04fabe9dbb4cd67e4d59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.998ex; height:2.843ex;" alt="{\displaystyle \ f(x)}"></span>. </p><p>Din il-funzjoni ġdida niddenotawha b’ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ g\circ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>g</mi> <mo>∘</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ g\circ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de0feb0dc49fcc1703786abd5e5d4f4a55005a15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.17ex; height:2.509ex;" alt="{\displaystyle \ g\circ f}"></span>. Jekk nużaw in-notazzjoni tradizzjonali nistgħu niktbu hekk: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,(g\circ f)(x)=g[f(x)]\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>g</mi> <mo>∘</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>g</mi> <mo stretchy="false">[</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,(g\circ f)(x)=g[f(x)]\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2eab97490f7e22d8cf140ef065ea8d0dc10fba9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.237ex; height:2.843ex;" alt="{\displaystyle \,(g\circ f)(x)=g[f(x)]\,}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Notazzjonijiet_għall-funzjonijiet"><span id="Notazzjonijiet_g.C4.A7all-funzjonijiet"></span>Notazzjonijiet għall-funzjonijiet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=5" title="Editja s-sezzjoni: Notazzjonijiet għall-funzjonijiet" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=5" title="Edit section's source code: Notazzjonijiet għall-funzjonijiet"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jistgħu jintużaw notazzjonijiet oħra għall-valur ta’ funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cda729f4fc92e3228240eb588757ff43659c974" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.321ex; height:2.176ex;" alt="{\displaystyle \ F}"></span> li jikkorrispondi ma’ element <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9923068b5684340554217dfc8b2b968523527d9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.91ex; height:1.676ex;" alt="{\displaystyle \ x}"></span>, iddenotat fin-notazzjoni tradizzjonali b’<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ F(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98cf176d608f36193dd3bb15b4501f367550e940" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.46ex; height:2.843ex;" alt="{\displaystyle \ F(x)}"></span>: </p><p>F'dik li nsejħulha <b>notazzjoni b’funzjoni prefissa</b> niktbu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,Fx:=F(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>F</mi> <mi>x</mi> <mo>:=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,Fx:=F(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3579067fb0d265a2c1120e0c3d4afc8fb272c435" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.47ex; height:2.843ex;" alt="{\displaystyle \,Fx:=F(x)\,}"></span> .</dd></dl> <p>F'dik li nsejħulha <b>notazzjoni b’funzjoni suffissa</b> niktbu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,xF:=F(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>x</mi> <mi>F</mi> <mo>:=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,xF:=F(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f8d4f7ba29a322bcf97f7f4a3d1052b694e2714" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.47ex; height:2.843ex;" alt="{\displaystyle \,xF:=F(x)\,}"></span> .</dd></dl> <p>B’dawn in-notazzjonijiet il-kompożizzjoni ta’ żewġ funzjonijiet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cda729f4fc92e3228240eb588757ff43659c974" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.321ex; height:2.176ex;" alt="{\displaystyle \ F}"></span> u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f38cbd6027cb9c78d50514eca99aa8d23370669" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.407ex; height:2.176ex;" alt="{\displaystyle \ G}"></span> jistgħu jinkitbu f’4 modi: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,(F\circ G)x=G(Fx)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>F</mi> <mo>∘</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mi>x</mi> <mo>=</mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,(F\circ G)x=G(Fx)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/127c4b4861ddee22e06c408e876a3053eb4cc2bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.48ex; height:2.843ex;" alt="{\displaystyle \,(F\circ G)x=G(Fx)\,}"></span> ,</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,(F\circ G)x=F(Gx)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mi>F</mi> <mo>∘</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mi>x</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>G</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,(F\circ G)x=F(Gx)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/902312041139298500b2fa5fc7444590ae2e4d6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.48ex; height:2.843ex;" alt="{\displaystyle \,(F\circ G)x=F(Gx)\,}"></span> ,</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,x(F\circ G)=(xF)G\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>x</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mo>∘</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>F</mi> <mo stretchy="false">)</mo> <mi>G</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,x(F\circ G)=(xF)G\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97b3a3dbc56ab651f3b796f8e98b53f1dcb37c64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.48ex; height:2.843ex;" alt="{\displaystyle \,x(F\circ G)=(xF)G\,}"></span> ,</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,x(F\circ G)=(xG)F\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>x</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mo>∘</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mi>G</mi> <mo stretchy="false">)</mo> <mi>F</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,x(F\circ G)=(xG)F\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1d062f61764d0806a366b26132429130af2580" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.48ex; height:2.843ex;" alt="{\displaystyle \,x(F\circ G)=(xG)F\,}"></span> .</dd></dl> <p>Xi drabi minflok parentesi tondi jintużaw parentesi kwadri: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,F[x]=F(x)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>F</mi> <mo stretchy="false">[</mo> <mi>x</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,F[x]=F(x)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dea0eb13e3cde69a90e0b275f5d7a0357f6dae0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.117ex; height:2.843ex;" alt="{\displaystyle \,F[x]=F(x)\,}"></span> .</dd></dl> <p>B’dan il-mod nevitaw il-konfużjoni mal-parentesi li juru l-ordni ta’ l-operazzjonijiet. Fost oħrajn din in-notazzjoni tintuża f’xi programmi ta’ kalkulu simboliku. </p> <div class="mw-heading mw-heading3"><h3 id="Funzjonijiet_ta’_żewġ_varjabbli_jew_iżjed"><span id="Funzjonijiet_ta.E2.80.99_.C5.BCew.C4.A1_varjabbli_jew_i.C5.BCjed"></span>Funzjonijiet ta’ żewġ varjabbli jew iżjed</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=6" title="Editja s-sezzjoni: Funzjonijiet ta’ żewġ varjabbli jew iżjed" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=6" title="Edit section's source code: Funzjonijiet ta’ żewġ varjabbli jew iżjed"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Meta d-dominju ta' funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> ikun il-<a href="/w/index.php?title=Prodott_karte%C5%BCjan&action=edit&redlink=1" class="new" title="Prodott karteżjan (il-paġna ma teżistix)">prodott karteżjan</a> ta' żewġ settijiet u hekk il-funzjoni taġixxi fuq koppji ta’ elementi ta’ settijiet l-immaġini tal-koppja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/519ebc7fb09517eb852a7be5b74d760677156e10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.909ex; height:2.843ex;" alt="{\displaystyle \ (x,y)}"></span> nuruha bin-notazzjoni </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3abd4d91e7e7176cb9f28558b4e2c8c97282ea0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.188ex; height:2.843ex;" alt="{\displaystyle \ f(x,y)}"></span></dd></dl> <p>allavolja bin-notazzjoni introdotta fuq, suppost niktbu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f((x,y))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f((x,y))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/950f1c214d25ca2928eae8131131a1d8d841dafa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.997ex; height:2.843ex;" alt="{\displaystyle \ f((x,y))}"></span>. F'dal-kaz il-funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> tissejjaħ <b>funzjoni ta’ żewġ varjabbli</b>. </p><p>Pereżempju, il-funzjoni ta’ <a href="/wiki/Multiplikazzjoni" title="Multiplikazzjoni">multiplikazzjoni</a> tassoċja żewġ <a href="/w/index.php?title=Numri_naturali&action=edit&redlink=1" class="new" title="Numri naturali (il-paġna ma teżistix)">numri naturali</a> mal-prodott tagħhom: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f(x,y)=x\cdot y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mo>⋅</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f(x,y)=x\cdot y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68838b6738e91c4c8c9b0b2327094b65bb12ff44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.45ex; height:2.843ex;" alt="{\displaystyle \ f(x,y)=x\cdot y}"></span>. Din il-funzjoni nistgħu niddefinuha formalment bid-dominju <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \mathbb {N} \times \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {N} \times \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc924036db559d4d21047f7f34e7d93df215456" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.777ex; height:2.176ex;" alt="{\displaystyle \ \mathbb {N} \times \mathbb {N} }"></span>, is-sett tal-koppji tan-numri naturali kollha. </p><p>L-istess japplika jekk minflok żewġ settijiet nieħdu tlieta jew iżjed. </p> <div class="mw-heading mw-heading3"><h3 id="Funzjonijiet_ta’_iżjed_valuri"><span id="Funzjonijiet_ta.E2.80.99_i.C5.BCjed_valuri"></span>Funzjonijiet ta’ iżjed valuri</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=7" title="Editja s-sezzjoni: Funzjonijiet ta’ iżjed valuri" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=7" title="Edit section's source code: Funzjonijiet ta’ iżjed valuri"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jekk il-kodominju ta’ funzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> hu l-<a href="/w/index.php?title=Prodott_Carte%C5%BCjan&action=edit&redlink=1" class="new" title="Prodott Carteżjan (il-paġna ma teżistix)">prodott Carteżjan</a> ta' żewġ settijiet jew iżjed, dawk il-varjabbli spiss jinġabru f’vettur u nistgħu ngħidulha <b><a href="/w/index.php?title=Funzjoni_vettorjali&action=edit&redlink=1" class="new" title="Funzjoni vettorjali (il-paġna ma teżistix)">funzjoni vettorjali</a></b>. </p><p>Eżempju tipiku hu t-<a href="/w/index.php?title=Trasformazzjoni_linjari&action=edit&redlink=1" class="new" title="Trasformazzjoni linjari (il-paġna ma teżistix)">trasformazzjoni linjari</a> tal-<a href="/w/index.php?title=Pjan&action=edit&redlink=1" class="new" title="Pjan (il-paġna ma teżistix)">pjan</a>, pereżempju: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y)\to (y,x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y)\to (y,x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90391436d0aec6b4364e4d50ac050b361909d3cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.271ex; height:2.843ex;" alt="{\displaystyle (x,y)\to (y,x)}"></span>.</dd></dl> <p>Funzjoni ngħidulha <b><a href="/w/index.php?title=Funzjoni_polidroma&action=edit&redlink=1" class="new" title="Funzjoni polidroma (il-paġna ma teżistix)">polidroma</a></b> fil-każ li r-riżultat ta’ l-operazzjoni hu definit univokament: pereżempju, ir-<a href="/w/index.php?title=Radi%C4%8Bi_kwadrata&action=edit&redlink=1" class="new" title="Radiċi kwadrata (il-paġna ma teżistix)">radiċi kwadrata</a> ta’ <a href="/w/index.php?title=Numru_reali&action=edit&redlink=1" class="new" title="Numru reali (il-paġna ma teżistix)">numru reali</a> posittiv jinkiteb bħala l-funzjoni </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} _{+}\to \mathbb {P} (\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msub> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">P</mi> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} _{+}\to \mathbb {P} (\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/391feec867dc1092fed5cf8799b2aaad4b44208a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.711ex; height:2.843ex;" alt="{\displaystyle \mathbb {R} _{+}\to \mathbb {P} (\mathbb {R} )}"></span></dd></dl> <p>li tassoċja ma kull numru reali posittiv is-<a href="/w/index.php?title=Sett&action=edit&redlink=1" class="new" title="Sett (il-paġna ma teżistix)">sett</a> taż-żewġ radiċi kwadrati. Eżempju ieħor analogu hu l-<a href="/w/index.php?title=Logaritmu&action=edit&redlink=1" class="new" title="Logaritmu (il-paġna ma teżistix)">logaritmu</a> definit fuq is-sett tan-<a href="/w/index.php?title=Numri_komplessi&action=edit&redlink=1" class="new" title="Numri komplessi (il-paġna ma teżistix)">numri komplessi</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Operazzjonijiet_binarji">Operazzjonijiet binarji</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=8" title="Editja s-sezzjoni: Operazzjonijiet binarji" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=8" title="Edit section's source code: Operazzjonijiet binarji"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ħafna operazzjonijiet binarji ta’ l-aritmetika, bħal l-<a href="/w/index.php?title=Addizzjoni&action=edit&redlink=1" class="new" title="Addizzjoni (il-paġna ma teżistix)">addizzjoni</a> u l-<a href="/wiki/Multiplikazzjoni" title="Multiplikazzjoni">multiplikazzjoni</a>, huma funzjonijiet mill-prodott karteżjan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \mathbb {Z} \times \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {Z} \times \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26fdc3f25ef2aec291a4542dee283ef543431806" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.522ex; height:2.176ex;" alt="{\displaystyle \ \mathbb {Z} \times \mathbb {Z} }"></span> għal <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0481c80653b36238e4f4e79d8ab4ed225e5b7fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.131ex; height:2.176ex;" alt="{\displaystyle \ \mathbb {Z} }"></span>, u niddeskrivuhomu bin-<a href="/w/index.php?title=Notazzjoni_infissa&action=edit&redlink=1" class="new" title="Notazzjoni infissa (il-paġna ma teżistix)">notazzjoni infissa</a>: jiġifieri niktbu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x+y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x+y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf83e2980005ce971eb5e6a64d99a3ab4fc395a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.906ex; height:2.343ex;" alt="{\displaystyle \ x+y}"></span> (u mhux <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ +(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>+</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ +(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1429ff7c427784e3af35ae4bc3ab75f2e5c589c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.749ex; height:2.843ex;" alt="{\displaystyle \ +(x,y)}"></span>) biex niddeskrivu l-immagini tal-koppja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ (x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/519ebc7fb09517eb852a7be5b74d760677156e10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.909ex; height:2.843ex;" alt="{\displaystyle \ (x,y)}"></span> bl-operazzjoni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5320d3bfe8668fd5cc282df3134850ac2604e821" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.389ex; height:2.176ex;" alt="{\displaystyle \ +}"></span>. </p><p>Din in-notazzjoni ġiet ġeneralizzata fl-<a href="/wiki/Al%C4%A1ebra" title="Alġebra">alġebra</a> moderna, biex ikunu jistgħu jiġu definiti <a href="/w/index.php?title=Strutturi_al%C4%A1ebrin&action=edit&redlink=1" class="new" title="Strutturi alġebrin (il-paġna ma teżistix)">strutturi alġebrin</a> bħal pereżempju dik ta’ <a href="/wiki/Grupp" class="mw-disambig" title="Grupp">grupp</a>, bħala sett <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> mogħti xi operazzjonijiet binarji li għandhom propjetajiet determinati. </p> <div class="mw-heading mw-heading2"><h2 id="Klassifikazzjoni">Klassifikazzjoni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=9" title="Editja s-sezzjoni: Klassifikazzjoni" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=9" title="Edit section's source code: Klassifikazzjoni"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fil-matematika u sostanzjalment fl-applikazzjonijiet tagħha kollha niltaqgħu ma’ ħafna tipi ta’ funzjonijiet b’karatteristiċi diversi ħafna. L-għadd kbir tal-funzjonijiet għalhekk nikklassifikawha skond bosta kriteri. </p> <div class="mw-heading mw-heading3"><h3 id="Klassifikazzjoni_bbażata_purament_fuq_is-settijiet"><span id="Klassifikazzjoni_bba.C5.BCata_purament_fuq_is-settijiet"></span>Klassifikazzjoni bbażata purament fuq is-settijiet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=10" title="Editja s-sezzjoni: Klassifikazzjoni bbażata purament fuq is-settijiet" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=10" title="Edit section's source code: Klassifikazzjoni bbażata purament fuq is-settijiet"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_injettiva&action=edit&redlink=1" class="new" title="Funzjoni injettiva (il-paġna ma teżistix)">funzjoni injettiva</a></li> <li><a href="/w/index.php?title=Funzjoni_surjettiva&action=edit&redlink=1" class="new" title="Funzjoni surjettiva (il-paġna ma teżistix)">funzjoni surjettiva</a></li> <li><a href="/w/index.php?title=Funzjoni_bijettiva&action=edit&redlink=1" class="new" title="Funzjoni bijettiva (il-paġna ma teżistix)">funzjoni bijettiva</a></li> <li><a href="/w/index.php?title=Endofunzjoni&action=edit&redlink=1" class="new" title="Endofunzjoni (il-paġna ma teżistix)">endofunzjoni</a></li> <li><a href="/w/index.php?title=Permutazzjoni&action=edit&redlink=1" class="new" title="Permutazzjoni (il-paġna ma teżistix)">permutazzjoni</a></li> <li><a href="/w/index.php?title=Involuzzjoni&action=edit&redlink=1" class="new" title="Involuzzjoni (il-paġna ma teżistix)">involuzzjoni</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Klassifikazzjoni_bbażata_fuq_it-tip_ta’_dominju_u_kodominju"><span id="Klassifikazzjoni_bba.C5.BCata_fuq_it-tip_ta.E2.80.99_dominju_u_kodominju"></span>Klassifikazzjoni bbażata fuq it-tip ta’ dominju u kodominju</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=11" title="Editja s-sezzjoni: Klassifikazzjoni bbażata fuq it-tip ta’ dominju u kodominju" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=11" title="Edit section's source code: Klassifikazzjoni bbażata fuq it-tip ta’ dominju u kodominju"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_numerika&action=edit&redlink=1" class="new" title="Funzjoni numerika (il-paġna ma teżistix)">funzjoni numerika</a></li> <li><a href="/w/index.php?title=Funzjoni_diskreta&action=edit&redlink=1" class="new" title="Funzjoni diskreta (il-paġna ma teżistix)">funzjoni diskreta</a></li> <li><a href="/w/index.php?title=Su%C4%8B%C4%8Bessjoni&action=edit&redlink=1" class="new" title="Suċċessjoni (il-paġna ma teżistix)">suċċessjoni</a></li> <li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_varjabbli_reali&action=edit&redlink=1" class="new" title="Funzjoni ta’ varjabbli reali (il-paġna ma teżistix)">funzjoni ta’ varjabbli reali</a></li> <li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_varjabbli_komplessa&action=edit&redlink=1" class="new" title="Funzjoni ta’ varjabbli komplessa (il-paġna ma teżistix)">funzjoni ta’ varjabbli komplessa</a></li> <li><a href="/w/index.php?title=Morfi%C5%BCmu&action=edit&redlink=1" class="new" title="Morfiżmu (il-paġna ma teżistix)">morfiżmu</a></li> <li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_sett&action=edit&redlink=1" class="new" title="Funzjoni ta’ sett (il-paġna ma teżistix)">funzjoni ta’ sett</a></li> <li><a href="/w/index.php?title=Funzjoni_indikatri%C4%8Bi&action=edit&redlink=1" class="new" title="Funzjoni indikatriċi (il-paġna ma teżistix)">funzjoni indikatriċi</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Klassifikazzjoni_tal-funzjonijiet_mill-ambitu_tal-kalkulabbilià"><span id="Klassifikazzjoni_tal-funzjonijiet_mill-ambitu_tal-kalkulabbili.C3.A0"></span>Klassifikazzjoni tal-funzjonijiet mill-ambitu tal-kalkulabbilià</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=12" title="Editja s-sezzjoni: Klassifikazzjoni tal-funzjonijiet mill-ambitu tal-kalkulabbilià" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=12" title="Edit section's source code: Klassifikazzjoni tal-funzjonijiet mill-ambitu tal-kalkulabbilià"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_rikorsiva_primittiva&action=edit&redlink=1" class="new" title="Funzjoni rikorsiva primittiva (il-paġna ma teżistix)">funzjoni rikorsiva primittiva</a></li> <li><a href="/w/index.php?title=Funzjoni_kalkulabbli&action=edit&redlink=1" class="new" title="Funzjoni kalkulabbli (il-paġna ma teżistix)">funzjoni kalkulabbli</a></li> <li><a href="/w/index.php?title=Funzjoni_rikorsiva&action=edit&redlink=1" class="new" title="Funzjoni rikorsiva (il-paġna ma teżistix)">funzjoni rikorsiva</a></li> <li><a href="/w/index.php?title=Funzjoni_rikorsiva_totali&action=edit&redlink=1" class="new" title="Funzjoni rikorsiva totali (il-paġna ma teżistix)">funzjoni rikorsiva totali</a></li> <li><a href="/w/index.php?title=Funzjoni_enumerattiva&action=edit&redlink=1" class="new" title="Funzjoni enumerattiva (il-paġna ma teżistix)">funzjoni enumerattiva</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Klassifikazzjoni_tal-funzjonijiet_ta’_l-analisi_infiniteżmali"><span id="Klassifikazzjoni_tal-funzjonijiet_ta.E2.80.99_l-analisi_infinite.C5.BCmali"></span>Klassifikazzjoni tal-funzjonijiet ta’ l-analisi infiniteżmali</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=13" title="Editja s-sezzjoni: Klassifikazzjoni tal-funzjonijiet ta’ l-analisi infiniteżmali" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=13" title="Edit section's source code: Klassifikazzjoni tal-funzjonijiet ta’ l-analisi infiniteżmali"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_armonika&action=edit&redlink=1" class="new" title="Funzjoni armonika (il-paġna ma teżistix)">funzjoni armonika</a></li> <li><a href="/w/index.php?title=Funzjoni_kontinwa&action=edit&redlink=1" class="new" title="Funzjoni kontinwa (il-paġna ma teżistix)">funzjoni kontinwa</a></li> <li><a href="/w/index.php?title=Funzjoni_pari&action=edit&redlink=1" class="new" title="Funzjoni pari (il-paġna ma teżistix)">funzjoni pari</a> u <a href="/w/index.php?title=Funzjoni_dispari&action=edit&redlink=1" class="new" title="Funzjoni dispari (il-paġna ma teżistix)">funzjoni dispari</a></li> <li><a href="/w/index.php?title=Funzjoni_ti%C5%BCdied&action=edit&redlink=1" class="new" title="Funzjoni tiżdied (il-paġna ma teżistix)">funzjoni tiżdied</a>, <a href="/w/index.php?title=Funzjoni_tonqos&action=edit&redlink=1" class="new" title="Funzjoni tonqos (il-paġna ma teżistix)">funzjoni tonqos</a> u <a href="/w/index.php?title=Funzjoni_monotona&action=edit&redlink=1" class="new" title="Funzjoni monotona (il-paġna ma teżistix)">funzjoni monotona</a></li> <li><a href="/w/index.php?title=Funzjoni_polinomjali&action=edit&redlink=1" class="new" title="Funzjoni polinomjali (il-paġna ma teżistix)">funzjoni polinomjali</a></li> <li><a href="/w/index.php?title=Funzjoni_razzjonali_fratta&action=edit&redlink=1" class="new" title="Funzjoni razzjonali fratta (il-paġna ma teżistix)">funzjoni razzjonali fratta</a></li> <li><a href="/w/index.php?title=Funzjoni_traxendenti&action=edit&redlink=1" class="new" title="Funzjoni traxendenti (il-paġna ma teżistix)">funzjoni traxendenti</a></li> <li><a href="/w/index.php?title=Funzjoni_differenzjabbli&action=edit&redlink=1" class="new" title="Funzjoni differenzjabbli (il-paġna ma teżistix)">funzjoni differenzjabbli</a></li> <li><a href="/w/index.php?title=Funzjoni_lixxa&action=edit&redlink=1" class="new" title="Funzjoni lixxa (il-paġna ma teżistix)">funzjoni lixxa</a></li> <li><a href="/w/index.php?title=Funzjoni_analitika&action=edit&redlink=1" class="new" title="Funzjoni analitika (il-paġna ma teżistix)">funzjoni analitika</a></li> <li><a href="/w/index.php?title=Funzjoni_olomorfa&action=edit&redlink=1" class="new" title="Funzjoni olomorfa (il-paġna ma teżistix)">funzjoni olomorfa</a></li> <li><a href="/w/index.php?title=Funzjoni_antjolomorfa&action=edit&redlink=1" class="new" title="Funzjoni antjolomorfa (il-paġna ma teżistix)">funzjoni antjolomorfa</a></li> <li><a href="/w/index.php?title=Funzjoni_meromorfa&action=edit&redlink=1" class="new" title="Funzjoni meromorfa (il-paġna ma teżistix)">funzjoni meromorfa</a></li> <li><a href="/w/index.php?title=Funzjoni_konvessa&action=edit&redlink=1" class="new" title="Funzjoni konvessa (il-paġna ma teżistix)">funzjoni konvessa</a></li> <li><a href="/w/index.php?title=Funzjoni_integrali&action=edit&redlink=1" class="new" title="Funzjoni integrali (il-paġna ma teżistix)">funzjoni integrali</a></li> <li><a href="/w/index.php?title=Funzjoni_%C4%8Bilindrika&action=edit&redlink=1" class="new" title="Funzjoni ċilindrika (il-paġna ma teżistix)">funzjoni ċilindrika</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Xi_funzjonijiet_magħrufa"><span id="Xi_funzjonijiet_mag.C4.A7rufa"></span>Xi funzjonijiet magħrufa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=14" title="Editja s-sezzjoni: Xi funzjonijiet magħrufa" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=14" title="Edit section's source code: Xi funzjonijiet magħrufa"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_Beta&action=edit&redlink=1" class="new" title="Funzjoni Beta (il-paġna ma teżistix)">funzjoni Beta</a>, <a href="/w/index.php?title=Funzjoni_Gamma&action=edit&redlink=1" class="new" title="Funzjoni Gamma (il-paġna ma teżistix)">funzjoni Gamma</a></li> <li><a href="/w/index.php?title=Funzjonijiet_trigonometri%C4%8Bi&action=edit&redlink=1" class="new" title="Funzjonijiet trigonometriċi (il-paġna ma teżistix)">funzjonijiet trigonometriċi</a>: <a href="/w/index.php?title=Senu&action=edit&redlink=1" class="new" title="Senu (il-paġna ma teżistix)">senu</a>, <a href="/w/index.php?title=Kosenu&action=edit&redlink=1" class="new" title="Kosenu (il-paġna ma teżistix)">kosenu</a>, <a href="/w/index.php?title=Tan%C4%A1ent&action=edit&redlink=1" class="new" title="Tanġent (il-paġna ma teżistix)">tanġent</a>, <a href="/w/index.php?title=Kotan%C4%A1ent&action=edit&redlink=1" class="new" title="Kotanġent (il-paġna ma teżistix)">kotanġent</a></li> <li><a href="/w/index.php?title=Funzjoni_identit%C3%A0&action=edit&redlink=1" class="new" title="Funzjoni identità (il-paġna ma teżistix)">funzjoni identità</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Funzjonijiet_ta’_interess_probabilistiku_u_statistiku"><span id="Funzjonijiet_ta.E2.80.99_interess_probabilistiku_u_statistiku"></span>Funzjonijiet ta’ interess probabilistiku u statistiku</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Funzjonijiet_(matematika)&veaction=edit&section=15" title="Editja s-sezzjoni: Funzjonijiet ta’ interess probabilistiku u statistiku" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Funzjonijiet_(matematika)&action=edit&section=15" title="Edit section's source code: Funzjonijiet ta’ interess probabilistiku u statistiku"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_ripartizzjoni&action=edit&redlink=1" class="new" title="Funzjoni ta’ ripartizzjoni (il-paġna ma teżistix)">Funzjoni ta’ ripartizzjoni</a></li> <li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_probabbilt%C3%A0&action=edit&redlink=1" class="new" title="Funzjoni ta’ probabbiltà (il-paġna ma teżistix)">Funzjoni ta’ probabbiltà</a></li> <li><a href="/w/index.php?title=Funzjoni_ta%E2%80%99_densit%C3%A0&action=edit&redlink=1" class="new" title="Funzjoni ta’ densità (il-paġna ma teżistix)">Funzjoni ta’ densità</a></li> <li><a href="/w/index.php?title=Funzjoni_%C4%A1eneratri%C4%8Bi_tal-momenti&action=edit&redlink=1" class="new" title="Funzjoni ġeneratriċi tal-momenti (il-paġna ma teżistix)">Funzjoni ġeneratriċi tal-momenti</a></li> <li><a href="/w/index.php?title=Funzjoni_karatteristika&action=edit&redlink=1" class="new" title="Funzjoni karatteristika (il-paġna ma teżistix)">Funzjoni karatteristika</a></li></ul> <p><br /> </p> <div class="tright portal" style="border:solid #aaa 1px;margin:0.5em 0 0.5em 0.5em;"> <table style="background:#f9f9f9; font-size:85%; line-height:110%;"> <tbody><tr> <td><span 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