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class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Beginning</div> </a> </li> <li id="toc-Hiikkaa_Warroomii_fi_Akkaataawan_Warroomii_itti_bareessan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hiikkaa_Warroomii_fi_Akkaataawan_Warroomii_itti_bareessan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Hiikkaa Warroomii fi Akkaataawan Warroomii itti bareessan</span> </div> </a> <button aria-controls="toc-Hiikkaa_Warroomii_fi_Akkaataawan_Warroomii_itti_bareessan-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>Toggle Hiikkaa Warroomii fi Akkaataawan Warroomii itti bareessan subsection</span> </button> <ul id="toc-Hiikkaa_Warroomii_fi_Akkaataawan_Warroomii_itti_bareessan-sublist" class="vector-toc-list"> <li id="toc-Warroomii_barreessu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Warroomii_barreessu"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Warroomii barreessu</span> </div> </a> <ul id="toc-Warroomii_barreessu-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Warroomii_Ibsuu:" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Warroomii_Ibsuu:"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Warroomii Ibsuu:</span> </div> </a> <ul id="toc-Warroomii_Ibsuu:-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hiika_jechoota_yaad-rimeewarroomiin_walqabatan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hiika_jechoota_yaad-rimeewarroomiin_walqabatan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Hiika jechoota yaad-rimeewarroomiin walqabatan</span> </div> </a> <ul id="toc-Hiika_jechoota_yaad-rimeewarroomiin_walqabatan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Garagalchoo_fi_Icciitii_Warroomiiwwan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Garagalchoo_fi_Icciitii_Warroomiiwwan"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Garagalchoo fi Icciitii Warroomiiwwan</span> </div> </a> <button aria-controls="toc-Garagalchoo_fi_Icciitii_Warroomiiwwan-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>Toggle Garagalchoo fi Icciitii Warroomiiwwan subsection</span> </button> <ul id="toc-Garagalchoo_fi_Icciitii_Warroomiiwwan-sublist" class="vector-toc-list"> <li id="toc-Garagalchoo_Warroomii_(inverse_function)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Garagalchoo_Warroomii_(inverse_function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Garagalchoo Warroomii (inverse function)</span> </div> </a> <ul id="toc-Garagalchoo_Warroomii_(inverse_function)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Warroomii_Icciitii(Implicit_Function)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Warroomii_Icciitii(Implicit_Function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Warroomii Icciitii(Implicit Function)</span> </div> </a> <ul id="toc-Warroomii_Icciitii(Implicit_Function)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Amaloota_Warroomii" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Amaloota_Warroomii"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Amaloota Warroomii</span> </div> </a> <button aria-controls="toc-Amaloota_Warroomii-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>Toggle Amaloota Warroomii subsection</span> </button> <ul id="toc-Amaloota_Warroomii-sublist" class="vector-toc-list"> <li id="toc-Warroomiiwwan_Daaddeessaa(Standard_Function):" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Warroomiiwwan_Daaddeessaa(Standard_Function):"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Warroomiiwwan Daaddeessaa(Standard Function):</span> </div> </a> <ul id="toc-Warroomiiwwan_Daaddeessaa(Standard_Function):-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Walseennoo_Warroomii_(composition_function)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Walseennoo_Warroomii_(composition_function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Walseennoo Warroomii (composition function)</span> </div> </a> <ul id="toc-Walseennoo_Warroomii_(composition_function)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Warroomii_Tokko_tokkof,_Warroomii_tokko_tokkof_gitaa,_warroomii_irratti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Warroomii_Tokko_tokkof,_Warroomii_tokko_tokkof_gitaa,_warroomii_irratti"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Warroomii Tokko tokkof, Warroomii tokko tokkof gitaa, warroomii irratti</span> </div> </a> <ul id="toc-Warroomii_Tokko_tokkof,_Warroomii_tokko_tokkof_gitaa,_warroomii_irratti-sublist" class="vector-toc-list"> <li id="toc-Warroomii_Tokko_tokkof_(one_to_one_function)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Warroomii_Tokko_tokkof_(one_to_one_function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.1</span> <span>Warroomii Tokko tokkof (one to one function)</span> </div> </a> <ul id="toc-Warroomii_Tokko_tokkof_(one_to_one_function)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Warroomii_irratti_(on_to_function)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Warroomii_irratti_(on_to_function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.2</span> <span>Warroomii irratti (on to function)</span> </div> </a> <ul id="toc-Warroomii_irratti_(on_to_function)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Warroomii_tokko_tokkof_gitaa(one_to_one_corresponde_function)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Warroomii_tokko_tokkof_gitaa(one_to_one_corresponde_function)"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.3</span> <span>Warroomii tokko tokkof gitaa(one to one corresponde function)</span> </div> </a> <ul id="toc-Warroomii_tokko_tokkof_gitaa(one_to_one_corresponde_function)-sublist" class="vector-toc-list"> </ul> </li> </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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Warroomii (faankishinii)</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="Go to an article in another language. Available in 120 languages" > <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 languages</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 – Afrikoota" lang="af" hreflang="af" data-title="Funksie" data-language-autonym="Afrikaans" data-language-local-name="Afrikoota" 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) – Alemannic" lang="gsw" hreflang="gsw" data-title="Funktion (Mathematik)" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" 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 – Afaan Sidaamaa" lang="am" hreflang="am" data-title="አስረካቢ" data-language-autonym="አማርኛ" data-language-local-name="Afaan Sidaamaa" 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 – Aragonese" lang="an" hreflang="an" data-title="Función matematica" data-language-autonym="Aragonés" data-language-local-name="Aragonese" 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 – Arabiffaa" lang="ar" hreflang="ar" data-title="دالة" data-language-autonym="العربية" data-language-local-name="Arabiffaa" 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) – Afaan Azerbaijani" lang="az" hreflang="az" data-title="Funksiya (riyaziyyat)" data-language-autonym="Azərbaycanca" data-language-local-name="Afaan Azerbaijani" 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) – Afaan Belarusia" lang="be" hreflang="be" data-title="Функцыя (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="Afaan Belarusia" 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 – Afaan Bulgariya" lang="bg" hreflang="bg" data-title="Функция" data-language-autonym="Български" data-language-local-name="Afaan Bulgariya" 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) – Afaan Baangladeshi" lang="bn" hreflang="bn" data-title="অপেক্ষক (গণিত)" data-language-autonym="বাংলা" data-language-local-name="Afaan Baangladeshi" 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) – Afaan Bosniyaa" lang="bs" hreflang="bs" data-title="Funkcija (matematika)" data-language-autonym="Bosanski" data-language-local-name="Afaan Bosniyaa" 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 – Afaan Katalaa" lang="ca" hreflang="ca" data-title="Funció" data-language-autonym="Català" data-language-local-name="Afaan Katalaa" 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) – Central Kurdish" lang="ckb" hreflang="ckb" data-title="فانکشن (ماتماتیک)" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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) – Afaan Czech" lang="cs" hreflang="cs" data-title="Funkce (matematika)" data-language-autonym="Čeština" data-language-local-name="Afaan Czech" 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 – Welishiffaa" lang="cy" hreflang="cy" data-title="Ffwythiant" data-language-autonym="Cymraeg" data-language-local-name="Welishiffaa" 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) – Afaan Deenmaark" lang="da" hreflang="da" data-title="Funktion (matematik)" data-language-autonym="Dansk" data-language-local-name="Afaan Deenmaark" 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) – Afaan Jarmanii" lang="de" hreflang="de" data-title="Funktion (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="Afaan Jarmanii" 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 – Afaan Giriiki" lang="el" hreflang="el" data-title="Συνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="Afaan Giriiki" 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) – Ingliffa" lang="en" hreflang="en" data-title="Function (mathematics)" data-language-autonym="English" data-language-local-name="Ingliffa" 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) – Afaan Esperantoo" lang="eo" hreflang="eo" data-title="Funkcio (matematiko)" data-language-autonym="Esperanto" data-language-local-name="Afaan Esperantoo" 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) – Afaan Ispeen" lang="es" hreflang="es" data-title="Función (matemática)" data-language-autonym="Español" data-language-local-name="Afaan Ispeen" 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) – Afaan Istooniya" lang="et" hreflang="et" data-title="Funktsioon (matemaatika)" data-language-autonym="Eesti" data-language-local-name="Afaan Istooniya" 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) – Afaan Baskuu" lang="eu" hreflang="eu" data-title="Funtzio (matematika)" data-language-autonym="Euskara" data-language-local-name="Afaan Baskuu" 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 – Afaan Persia" lang="fa" hreflang="fa" data-title="تابع" data-language-autonym="فارسی" data-language-local-name="Afaan Persia" 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 – Afaan Fiilaandi" lang="fi" hreflang="fi" data-title="Funktio" data-language-autonym="Suomi" data-language-local-name="Afaan Fiilaandi" 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) – Fijian" lang="fj" hreflang="fj" data-title="Cakacaka (fika)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" 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 – Afaan Faroese" lang="fo" hreflang="fo" data-title="Funksjón" data-language-autonym="Føroyskt" data-language-local-name="Afaan 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) – Afaan Faransaayii" lang="fr" hreflang="fr" data-title="Fonction (mathématiques)" data-language-autonym="Français" data-language-local-name="Afaan Faransaayii" 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) – Afaan Ayirishii" lang="ga" hreflang="ga" data-title="Feidhm (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="Afaan Ayirishii" 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 – Afaan Galishii" lang="gl" hreflang="gl" data-title="Función" data-language-autonym="Galego" data-language-local-name="Afaan Galishii" 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 – Afaan Hebrew" lang="he" hreflang="he" data-title="פונקציה" data-language-autonym="עברית" data-language-local-name="Afaan Hebrew" 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 – Afaan Hindii" lang="hi" hreflang="hi" data-title="फलन" data-language-autonym="हिन्दी" data-language-local-name="Afaan Hindii" 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) – Afaan Croatian" lang="hr" hreflang="hr" data-title="Funkcija (matematika)" data-language-autonym="Hrvatski" data-language-local-name="Afaan Croatian" 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) – Afaan Hangaari" lang="hu" hreflang="hu" data-title="Függvény (matematika)" data-language-autonym="Magyar" data-language-local-name="Afaan Hangaari" 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) – Armenian" lang="hy" hreflang="hy" data-title="Ֆունկցիա (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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) – Afaan Indoneziya" lang="id" hreflang="id" data-title="Fungsi (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Afaan Indoneziya" 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) – Ayiislandiffaa" lang="is" hreflang="is" data-title="Fall (stærðfræði)" data-language-autonym="Íslenska" data-language-local-name="Ayiislandiffaa" 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) – Afaan Xaaliyaani" lang="it" hreflang="it" data-title="Funzione (matematica)" data-language-autonym="Italiano" data-language-local-name="Afaan Xaaliyaani" 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) – Afaan Japanii" lang="ja" hreflang="ja" data-title="関数 (数学)" data-language-autonym="日本語" data-language-local-name="Afaan Japanii" 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) – Afaan Georgian" lang="ka" hreflang="ka" data-title="ფუნქცია (მათემატიკა)" data-language-autonym="ქართული" data-language-local-name="Afaan Georgian" 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) – Kabyle" lang="kab" hreflang="kab" data-title="Tasɣent (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" 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) – Kazakh" lang="kk" hreflang="kk" data-title="Функция (математика)" data-language-autonym="Қазақша" data-language-local-name="Kazakh" 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 – Afaan Korea" lang="ko" hreflang="ko" data-title="함수" data-language-autonym="한국어" data-language-local-name="Afaan Korea" 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 – Afaan Laatini" lang="la" hreflang="la" data-title="Functio" data-language-autonym="Latina" data-language-local-name="Afaan Laatini" 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) – Luxembourgish" lang="lb" hreflang="lb" data-title="Funktioun (Mathematik)" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" 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) – Lao" lang="lo" hreflang="lo" data-title="ຕຳລາ (ຄະນິດສາດ)" data-language-autonym="ລາວ" data-language-local-name="Lao" 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) – Afaan Liituniyaa" lang="lt" hreflang="lt" data-title="Funkcija (matematika)" data-language-autonym="Lietuvių" data-language-local-name="Afaan Liituniyaa" 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 – Afaan Lativiyaa" lang="lv" hreflang="lv" data-title="Funkcija" data-language-autonym="Latviešu" data-language-local-name="Afaan Lativiyaa" 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) – Afaan Macedooniyaa" lang="mk" hreflang="mk" data-title="Функција (математика)" data-language-autonym="Македонски" data-language-local-name="Afaan Macedooniyaa" 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 – Malayaalamiffaa" lang="ml" hreflang="ml" data-title="ഫങ്ഷൻ" data-language-autonym="മലയാളം" data-language-local-name="Malayaalamiffaa" 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) – Mongolian" lang="mn" hreflang="mn" data-title="Функц (математик)" data-language-autonym="Монгол" data-language-local-name="Mongolian" 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) – Afaan Maratii" lang="mr" hreflang="mr" data-title="फल (गणित)" data-language-autonym="मराठी" data-language-local-name="Afaan Maratii" 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 – Malaayiffaa" lang="ms" hreflang="ms" data-title="Fungsi" data-language-autonym="Bahasa Melayu" data-language-local-name="Malaayiffaa" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Funzjonijiet_(matematika)" title="Funzjonijiet (matematika) – Afaan Maltesii" lang="mt" hreflang="mt" data-title="Funzjonijiet (matematika)" data-language-autonym="Malti" data-language-local-name="Afaan Maltesii" class="interlanguage-link-target"><span>Malti</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 – Burmese" lang="my" hreflang="my" data-title="ဖန်ရှင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" 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) – Low German" lang="nds" hreflang="nds" data-title="Afbillen (Mathematik)" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" 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) – Afaan Dachii" lang="nl" hreflang="nl" data-title="Functie (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="Afaan Dachii" 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 – Afaan Norwegian" lang="nn" hreflang="nn" data-title="Matematisk funksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Afaan Norwegian" 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) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Funksjon (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" 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) – Afaan Occit" lang="oc" hreflang="oc" data-title="Aplicacion (matematicas)" data-language-autonym="Occitan" data-language-local-name="Afaan Occit" class="interlanguage-link-target"><span>Occitan</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) – Afaan Punjabii" lang="pa" hreflang="pa" data-title="ਫੰਕਸ਼ਨ (ਹਿਸਾਬ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Afaan Punjabii" 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 – Afaan Polandii" lang="pl" hreflang="pl" data-title="Funkcja" data-language-autonym="Polski" data-language-local-name="Afaan Polandii" 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) – Afaan Porchugaal" lang="pt" hreflang="pt" data-title="Função (matemática)" data-language-autonym="Português" data-language-local-name="Afaan Porchugaal" 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 – Afaan Romaniyaa" lang="ro" hreflang="ro" data-title="Funcție" data-language-autonym="Română" data-language-local-name="Afaan Romaniyaa" 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) – Afaan Rushiyaa" lang="ru" hreflang="ru" data-title="Функция (математика)" data-language-autonym="Русский" data-language-local-name="Afaan Rushiyaa" 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 – Yakut" lang="sah" hreflang="sah" data-title="Функция. Функция чэрчитэ, суолталарын түмсээнэ" data-language-autonym="Саха тыла" data-language-local-name="Yakut" 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) – Sicilian" lang="scn" hreflang="scn" data-title="Funzioni (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" 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) – Scots" lang="sco" hreflang="sco" data-title="Function (mathematics)" data-language-autonym="Scots" data-language-local-name="Scots" 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-Croatian" lang="sh" hreflang="sh" data-title="Funkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" 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) – Afaan Slovak" lang="sk" hreflang="sk" data-title="Zobrazenie (matematika)" data-language-autonym="Slovenčina" data-language-local-name="Afaan Slovak" 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) – Afaan Islovaniyaa" lang="sl" hreflang="sl" data-title="Funkcija (matematika)" data-language-autonym="Slovenščina" data-language-local-name="Afaan Islovaniyaa" 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 – Afaan Albaniyaa" lang="sq" hreflang="sq" data-title="Funksioni" data-language-autonym="Shqip" data-language-local-name="Afaan Albaniyaa" 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) – Afaan Serbiya" lang="sr" hreflang="sr" data-title="Функција (математика)" data-language-autonym="Српски / srpski" data-language-local-name="Afaan Serbiya" 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) – Afaan Sudaanii" lang="su" hreflang="su" data-title="Fungsi (matematika)" data-language-autonym="Sunda" data-language-local-name="Afaan Sudaanii" 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 – Afaan Suwidiin" lang="sv" hreflang="sv" data-title="Funktion" data-language-autonym="Svenska" data-language-local-name="Afaan Suwidiin" 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 – Afaan Tamilii" lang="ta" hreflang="ta" data-title="சார்பு" data-language-autonym="தமிழ்" data-language-local-name="Afaan Tamilii" 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) – Afaan Tayii" lang="th" hreflang="th" data-title="ฟังก์ชัน (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="Afaan Tayii" 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 – Afaan Turkii" lang="tr" hreflang="tr" data-title="Fonksiyon" data-language-autonym="Türkçe" data-language-local-name="Afaan Turkii" 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) – Afaan Ukreenii" lang="uk" hreflang="uk" data-title="Функція (математика)" data-language-autonym="Українська" data-language-local-name="Afaan Ukreenii" 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) – Afaan Urdu" lang="ur" hreflang="ur" data-title="تفاعل (ریاضیات)" data-language-autonym="اردو" data-language-local-name="Afaan 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) – Afaan Uzbek" lang="uz" hreflang="uz" data-title="Funksiya (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Afaan 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 – Afaan Veetinam" lang="vi" hreflang="vi" data-title="Hàm số" data-language-autonym="Tiếng Việt" data-language-local-name="Afaan Veetinam" 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) – Standard Moroccan Tamazight" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵙⵖⵏⵜ (ⵜⵓⵙⵏⴰⴽⵜ)" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Standard Moroccan Tamazight" 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 – Chinese" lang="zh" hreflang="zh" data-title="函数" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%98%A0%E5%B0%84" title="映射 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="映射" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/H%C3%A2m-s%C3%B2%CD%98" title="Hâm-sò͘ – Minnan" lang="nan" hreflang="nan" data-title="Hâm-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%87%BD%E6%95%B8" title="函數 – Cantonese" lang="yue" hreflang="yue" data-title="函數" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11348#sitelinks-wikipedia" title="Geessitu afaani gara afaani gulaali" class="wbc-editpage">Geessituuwwan gulaali</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Iddoowwan maqaa"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > 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Mee f'n hariiroo dha haa jennu. f'n Warroomiidha kan jennu (x,y), fi (x,w) miseensa f taanaan y=w yoo ta'e dha. Fkn: H=(1,3),(4,3),(5,3),(0,3) , H=(x,y):y=x^2 Warroomii dha. </p><p>Cimdiin tartii (a; b) miseensa hariiroo H yoo ta'e, a 'n seentuu jalqabaa yoo jedhamu b'n immoo seentuu lammaffaa jedhama. Kana keessatti sentuun jalqabaa mandhee(Domain) H yoo ta'u, seentuun lammaffaa immoo Hangii(Range) H jedhama. </p><p>Yoo haalli Mandhee fi haalli Hangii lakkoofsota dhugaa ta’anii fi galtee bifa Unkee armaan gadiitiin barreeffame <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=x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad1108c4c9ee8ac7de90b77f9bd27415b13b6bf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.638ex; height:3.009ex;" alt="{\displaystyle y=x^{2}}"></span> Haalli kun akka armaan gadiitti kan barreeffame akkaataa barreeffama qajeelfama keeyyata sadan armaan oliitiin: </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 \left(\mathbb {R} ,\mathbb {R} ,\left\{\left(x,x^{2}\right):x\in \mathbb {R} \right\}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo>,</mo> <mrow> <mo>{</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>,</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <mi>x</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mrow> <mo>}</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(\mathbb {R} ,\mathbb {R} ,\left\{\left(x,x^{2}\right):x\in \mathbb {R} \right\}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4de44e60df9a39903ee0af7163e93329dba622c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:24.927ex; height:3.343ex;" alt="{\displaystyle \left(\mathbb {R} ,\mathbb {R} ,\left\{\left(x,x^{2}\right):x\in \mathbb {R} \right\}\right)}"></span>, .</dd></dl> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hiikkaa_Warroomii_fi_Akkaataawan_Warroomii_itti_bareessan">Hiikkaa Warroomii fi Akkaataawan Warroomii itti bareessan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=1" title="Kutaa gulaali: Hiikkaa Warroomii fi Akkaataawan Warroomii itti bareessan" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=1" title="Edit section's source code: Hiikkaa Warroomii fi Akkaataawan Warroomii itti bareessan"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Warroomiin tuuta X irraa gara tuuta Y ramaddii miseensa Y tokkoon tokkoo miseensa X. Tuutni X madhee warroomichaa jedhama, tuuta Y immoo madheewa (codomain) warroomichaa jedhama. Akka idileetti, Warroomiin f: X → Y seera tokkoon tokkoon x X keessatti y adda Y keessatti ramaduudha. </p> <div class="mw-heading mw-heading3"><h3 id="Warroomii_barreessu">Warroomii barreessu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=2" title="Kutaa gulaali: Warroomii barreessu" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=2" title="Edit section's source code: Warroomii barreessu"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Warroomiin akaatawwan armaan gadiitiin barreffamuu danda'uu </p><p><b>Sirnaasxaa Xiyyaa:</b> Karaan beekamaan Warroomii bakka bu'uuf xiyya tuuta madhee fi madheewa gidduutti fayyadamuudha. </p><p><b>Sirnaasxaa Kasaa(index):</b> Warroomiiwwanis jalarfii(subscript) fayyadamuun ibsamuu danda'u. Fakkeenyaaf, f<sub>1</sub> tartiiba Warroomii keessatti Warroomii jalqabaa bakka bu’a. </p><p><b>Sirnaasxaa Tuqaa:</b> Haala tokko tokko keessatti, Warroomiiwwan tuqaa fayyadamuun, kan akka f(x). ykn g(x) fayyadamuun agarsiifamuu danda'u. </p><p><b>Sirnaasxaa addaa</b>: Dirreewwan herregaa adda addaa Warroomiif Sirnaasxaa addaa fayyadamu, kan akka Sirnaasxaa sigmaa (∑) walitti qabama keessatti yookiin Sirnaasxaa intagiraalii ykn Wajjuumee (∫) kaalkulasii keessatti. </p><p><b>Sirnaasxaa Unkeen</b>: mala beekamaa warroomiiwwan herrega keessatti bakka bu’uudha. Mallattoolee fi qoyyaboota aljebraa fayyadamuun warroomii tokko ibsuu of keessaa qaba. </p><p><b>Sirnaasxaa Caattoo(graph notation):</b> mala warroomiiwwan herrega keessatti siiqqeewwan x fi y fayyadamuun ibsuuti </p> <table class="wikitable" align="center"> <tbody><tr> <th>Unkee </th> <th>Unkee gabaaba </th> <th>Gabatee </th> <th>Caattoo </th> <th>Caasoo veeniin </th></tr> <tr> <td><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{aligned}f\colon \mathbb {R} &\to \mathbb {R} \\x&\mapsto \ 2x\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mtd> <mtd> <mi></mi> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo stretchy="false">↦</mo> <mtext> </mtext> <mn>2</mn> <mi>x</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}f\colon \mathbb {R} &\to \mathbb {R} \\x&\mapsto \ 2x\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97176898139f75e5111defd683cdc5c31b139b71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.429ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}f\colon \mathbb {R} &\to \mathbb {R} \\x&\mapsto \ 2x\end{aligned}}}"></span> </td> <td><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{aligned}\ f(x)=\ 2x\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mtext> </mtext> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mtext> </mtext> <mn>2</mn> <mi>x</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\ f(x)=\ 2x\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2776060adfc4a7cafddc6e2a89409a59d3a6dc86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.921ex; height:2.843ex;" alt="{\displaystyle {\begin{aligned}\ f(x)=\ 2x\end{aligned}}}"></span> </td> <td> <table cellspacing="0" cellpadding="3"> <tbody><tr> <td align="right" style="width:2ex; border-right:1px double black; border-bottom:1px solid black">x </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">1 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">2 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">3 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">4 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">5 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">6 </td> <td align="right" style="width:2ex; border-right:1px solid black; border-bottom:1px solid black">7 </td> <td align="right" style="width:2ex; border-bottom:1px solid black">… </td></tr> <tr> <td align="right" style="border-right:1px double black"><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"> <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/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> </td> <td align="right" style="border-right:1px solid black">2 </td> <td align="right" style="border-right:1px solid black">4 </td> <td align="right" style="border-right:1px solid black">6 </td> <td align="right" style="border-right:1px solid black">8 </td> <td align="right" style="border-right:1px solid black">10 </td> <td align="right" style="border-right:1px solid black">12 </td> <td align="right" style="border-right:1px solid black">14 </td> <td align="right">… </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/File:Variables_proporcionals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Variables_proporcionals.png/100px-Variables_proporcionals.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Variables_proporcionals.png/150px-Variables_proporcionals.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Variables_proporcionals.png/200px-Variables_proporcionals.png 2x" data-file-width="291" data-file-height="213" /></a></span> </td> <td><span typeof="mw:File"><a href="/wiki/File:Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg/100px-Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg.png" decoding="async" width="100" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg/150px-Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg/200px-Aplicaci%C3%B3n_2_inyectiva_sobreyectiva02.svg.png 2x" data-file-width="250" data-file-height="200" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Warroomii_Ibsuu:">Warroomii Ibsuu:</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=3" title="Kutaa gulaali: Warroomii Ibsuu:" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=3" title="Edit section's source code: Warroomii Ibsuu:"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Gatii warroomii Tarreessuudhaan</b>: Karaan tokko warroomii ibsuu gatiiwwan warroomii galtee adda addaatiif ifatti tarreessuudha. FakkeenyaafMee warroomii f: {1, 2, 3} → {a, b, c} kan f(1) = a, f(2) = b, fi f(3) = c tiin ibsame ilaali. warroomii kana gatiiwwan isaa tarreessuun ibsuu dandeenya: {(1, a), (2, b), (3, c)}. </p><p><b>Unkeen</b>: warroomiiwwan unkee herregaa fayyadamuunis ibsamuu danda’u. Fakkeenyaaf, f(x) = 2x + 3 </p> <div class="mw-heading mw-heading2"><h2 id="Hiika_jechoota_yaad-rimeewarroomiin_walqabatan">Hiika jechoota yaad-rimeewarroomiin walqabatan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=4" title="Kutaa gulaali: Hiika jechoota yaad-rimeewarroomiin walqabatan" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=4" title="Edit section's source code: Hiika jechoota yaad-rimeewarroomiin walqabatan"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Madhee(Domain)</b>: Madheen warroomii tuuta gatiiwwan galtee ta'uu danda'an hunda warroomichaati. Gatii warroomichi itti ibsamee fi hiika qabu bakka bu'a. Madheen tuuta kamiyyuu ta'uu danda'a, kan akka lakkoofsota dhugaa (c), <a href="/wiki/Lakkoofsa_Intiijarii" title="Lakkoofsa Intiijarii">lakkoofsota udummii</a> (ℤ), ykn tuuta murtaa'aa wantootaa. </p><p><b>Madheewa(Codomain)</b>: Madheewni warroomii tuuta gatiiwwan bu'aa argamuu warroomichaa ta'uu danda'an hunda of keessaa qabuudha. Tuuta warroomichi galteewwan isaa itti kaartaa godhu bakka bu'a. Madheewni tuuta kamiyyuu ta'uu danda'a, Madheen walfakkaata. </p><p><b>Hangii()</b>: Hangiin warroomii tuuta gatiiwwan bu'aa argamuu dhugaa hunda warroomichi oomishuuf agarsiisa. Innis tuuta xiqqaa madheewa kan gatiiwwan qabatamaan warroomichi argate of keessaa qabuudha. Jecha biraatiin, hangan tuuta gatiiwwan bu'aa argamuu ta'uu danda'an hunda kan warroomichi fudhachuu danda'uudha. </p><p><b>Hariiroo fi warroomii keessatti, koodomeeniin tuuta bu’aa hariiroo ykn warroomii kennamee ta’uu danda’u hunda ti. Yeroo tokko tokko, madheewan hamma warroomichaa wajjinis walqixa. Haa ta'u malee, hangii citatuuta madheewa ti.</b> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Variables_proporcionals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Variables_proporcionals.png/169px-Variables_proporcionals.png" decoding="async" width="169" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Variables_proporcionals.png/254px-Variables_proporcionals.png 1.5x, //upload.wikimedia.org/wikipedia/commons/4/47/Variables_proporcionals.png 2x" data-file-width="291" data-file-height="213" /></a><figcaption>Caattoo warroomii</figcaption></figure> <p><b>Caattoo kaasuu(Graph Plot)</b>:Caattoo kaasuun bakka bu’iinsa mul’ataa warroomii <a href="/wiki/Sirna_Diriiroo_Ko%E2%80%99oordineetotaa" title="Sirna Diriiroo Ko’oordineetotaa">sirna cimdii tartii</a> fayyadamuun agarsiisudha. caattoon warroomii akkaataa gatiiwwan galtee (yeroo baay'ee siiqqe x irratti) gatiiwwan baasaa walgitan (yeroo baay'ee siiqqe y irratti) wajjin akka walqabatan agarsiisa. Tokkoon tokkoon qabxii caattoo irratti lamaan galtee-ba'aa warroomichaa bakka bu'a. Giraafichi amala, akkaataa fi amaloota warroomichaa irratti hubannoo kennuu danda'a. </p> <div class="mw-heading mw-heading2"><h2 id="Garagalchoo_fi_Icciitii_Warroomiiwwan">Garagalchoo fi Icciitii Warroomiiwwan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=5" title="Kutaa gulaali: Garagalchoo fi Icciitii Warroomiiwwan" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=5" title="Edit section's source code: Garagalchoo fi Icciitii Warroomiiwwan"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Garagalchoo_Warroomii_(inverse_function)"><span id="Garagalchoo_Warroomii_.28inverse_function.29"></span>Garagalchoo Warroomii (inverse function)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=6" title="Kutaa gulaali: Garagalchoo Warroomii (inverse function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=6" title="Edit section's source code: Garagalchoo Warroomii (inverse function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inverse Function.png </p><p>Garagalchoon Warroomii  firoomsii(mapping) Warroomii biraa duubatti deebisudha. Warroomiin f kennameef, yoo Warroomiin biraa g kan f itti aanee g (ykn g f hordofee) hojiirra oolchuun galtee jalqabaa kennu jiraate, g Warroomii faallaa f jedhama. Jecha biraatiin, f(x) = y yoo ta’e, g(y) = x. sirnaasxaa Warroomii faallaa f yeroo baay’ee f<sup>-1</sup> jedhamee agarsiifama. </p><p>Garagalchoo warroomiin jiraachuuf, Warroomiin jalqabaa tokko tokkof(injective) ta'uu qaba, jechuunis tokkoon tokkoon gatii galtee gara gatii bu'aa argamuu addaatti firooma. Dabalataan, hangiin Warroomii jalqabaa madhee garagalchoo Warroomii  wajjin walsimuu qaba. </p><p>Fakkeenyaaf, yoo tarmiteriin ƒ teempireechara digrii seentigireedii C keessatti saagame gara Faareenhaayitii F tti jijjiire, deebii tarmiteriin kanaa ƒ−1 ta’a. Ho'a Faareenhaayitii F irraa gara Seelshiyaasii C tti deebisa jechuudha. </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 {\begin{aligned}f(C)&={\frac {9}{5}}C+32\\f^{-1}(F)&={\frac {5}{9}}(F-32)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>f</mi> <mo stretchy="false">(</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>9</mn> <mn>5</mn> </mfrac> </mrow> <mi>C</mi> <mo>+</mo> <mn>32</mn> </mtd> </mtr> <mtr> <mtd> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5</mn> <mn>9</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo>−</mo> <mn>32</mn> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}f(C)&={\frac {9}{5}}C+32\\f^{-1}(F)&={\frac {5}{9}}(F-32)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b31eb82a592e9d2d34a1eec4070ae1f7921309aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.536ex; margin-bottom: -0.302ex; width:21.767ex; height:10.843ex;" alt="{\displaystyle {\begin{aligned}f(C)&={\frac {9}{5}}C+32\\f^{-1}(F)&={\frac {5}{9}}(F-32)\end{aligned}}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Warroomii_Icciitii(Implicit_Function)"><span id="Warroomii_Icciitii.28Implicit_Function.29"></span>Warroomii Icciitii(Implicit Function)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=7" title="Kutaa gulaali: Warroomii Icciitii(Implicit Function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=7" title="Edit section's source code: Warroomii Icciitii(Implicit Function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Warroomii Icciitii: Warroomiin icciitii jechuun Warroomii walqixxaattoo jijjiiramaa tokko kanneen birootiin ifatti ibsuu dhiisuu danda’uun icciitiidhaan ibsameedha. Jecha biraatiin, Warroomiin implicit jijjiiramaa murtaa’eef ifatti osoo hin furin jijjiiramoota walqabsiisa. Hima walqixaa akkaataa addaatiin jijjiiramoota hedduu kan hammatu yoo ta’u jijjiiramoota hirkataa fi of danda’an lamaanuu of keessaa qabaachuu danda’a. </p><p>Fakkeenyaaf, hima walqixaa x^2 + y^2 = 1 icciitiidhaan geengoo yuunitii ibsa. Y tiif ifatti gama x yookiin faallaa kanaatiin kan hin furre ta’us, ammas hariiroo x fi y gidduu jiru geengoo irratti ibsa. </p> <div class="mw-heading mw-heading2"><h2 id="Amaloota_Warroomii">Amaloota Warroomii</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=8" title="Kutaa gulaali: Amaloota Warroomii" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=8" title="Edit section's source code: Amaloota Warroomii"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Warroomiiwwan_Daaddeessaa(Standard_Function):"><span id="Warroomiiwwan_Daaddeessaa.28Standard_Function.29:"></span>Warroomiiwwan Daaddeessaa(Standard Function):</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=9" title="Kutaa gulaali: Warroomiiwwan Daaddeessaa(Standard Function):" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=9" title="Edit section's source code: Warroomiiwwan Daaddeessaa(Standard Function):"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Isaan kun Warroomiiwwan foormulaawwanii fi amaloota akka gaariitti ibsaman kanneen akka Warroomiiwwan polinoomii, Warroomiiwwan eksaapooneenshiyaalii fi Warroomiiwwan tirigonoomeetirii qaban yeroo baay’ee itti fayyadamaniidha. </p><p><b>Warroomii Of-taasisaa(Identity):</b> Warroomiin oftaasisaan, f(x) = x jedhamee kan agarsiifamu, gatii galtee akka bu'aa argamuutti deebisa. Gatii jijjiiramaa ni eega. </p><p>Warroomiin Of-taasisaa gatii galtee eega: f(x) = x x hundaaf. </p><p>Warroomii Of-taasisaa Warroomii biraa kamiyyuu waliin qindeessuun Warroomii jalqabaa argamsiisa: f ∘ id = id ∘ f = f. </p><p><b>Warroomii Dhaabbataa:</b> Warroomiin dhaabbataa, kan akka f(x) = c, galtee x hundaaf gatii dhaabbataa c ramada. Galteen maal iyyuu yoo ta’e bu'aan walfakkaataadha.Warroomiiwwan dhaabbataa caattoo irratti sararoota qajeelaan ibsama. f(x) = c, </p><p><b>Warroomii Sararaawaa(linear)</b>: Warroomiin sararaawaa bifa f(x) = mx + b kan qabu yoo ta’u, m dhundula sararichaa kan agarsiisu yoo ta’u b immoo y-kutaa dha. caattoo irratti sarara qajeelaa ni uuma. </p><p><b>Warroomii kurmaanawaa (Kuwaadraatikii):</b> Warroomiin kuuwaadraatikii bifa f(x) = ax^2 + bx + c kan qabu yoo ta’u, a, b, fi c dhaabbataa dha. Yeroo giraafiin agarsiifamu paarabolaa bakka bu’a. </p><p><b>Warroomii aangeessoo(Ekspooneenshiyaalii):</b> Warroomiin eksaapooneenshiyaalii bifa f(x) = a^x qaba, maxxantuun a pozaatiivii ta’etti. Bu’aan akkuma x dabalaa deemuun eksaapooneenshiyaalii guddata. maxxantuun seelkoo (negative ) ta’etti. Bu’aan akkuma x hir'achaa deemuun eksaapooneenshiyaalii xiqaata. </p><p><b>Warroomii Loogaritmii</b>: Warroomiin loogaritmii bifa f(x) = log_a(x) qaba, bakka a dhaabbataa pozaatiivii ta’etti. Innis hojii faallaa Warroomii eksaapooneenshiyaalii bakka bu’a </p><p><b>Warroomiiwwan Rogkofa (Tirigonoomeetiri)</b>: Warroomiiwwan tirigonoomeetirii kan akka saayinii (sin), koosaayinii (cos), fi tangeentii (tan), kofoota fi cinaachawwan roga saddeetii sirrii ta’an keessatti walqabsiisu. Ji’oomeetirii fi kaalkulasii keessatti amaloota fi hojiirra oolmaa adda addaa qabu. </p><p><b>Warroomii Hundee Iskuweerii</b>: Warroomiin hundee iskuweerii, kan f(x) = √x jedhamee agarsiifamu, hundee iskuweerii negaatiivii hin taane lakkoofsa x deebisa. </p><p><b>Warroomii Gat-sirrii</b>: Warroomiin gat-sirrii, kan f(x) = |x| jedhamee agarsiifamu, fageenya lakkoofsa zeeroo irraa sarara lakkoofsaa irratti deebisa. </p><p><b>Warroomii Tarkaanfii</b>: Warroomiin tarkaanfii, Warroomii Heaviside jedhamuunis kan beekamu, gatii dhaabbataa gidduugaleessa keessatti kan qabuu fi qabxiilee ifteessaman irratti akka tasaa kan jijjiiramu dha. </p> <div class="mw-heading mw-heading3"><h3 id="Walseennoo_Warroomii_(composition_function)"><span id="Walseennoo_Warroomii_.28composition_function.29"></span>Walseennoo Warroomii (composition function)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=10" title="Kutaa gulaali: Walseennoo Warroomii (composition function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=10" title="Edit section's source code: Walseennoo Warroomii (composition function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Walseennoo Warroomii qoyyaba Warroomii lama walitti fiduun Warroomii haaraa uumuudha. Innis bu'aa Warroomii tokkoo fudhachuun akka galtee Warroomii biraatiif fayyadamuu of keessaa qaba. Walseennoon Warroomii lamaa f fi g akka (f ∘ g)(x) yookiin f(g(x))tti agarsiifama. Adeemsi walseennoo Warroomii akka armaan gadiitti ibsamuu danda’a: </p> <ol><li>Warroomiiwwan lama f fi g yoo kennameef, firii g galtee f tiif sirrii ta’uu isaa mirkaneessi. Kana jechuun domeeniin f hanga g of keessaa qabaachuu qaba.</li> <li>Gatii galtee x fudhadhuutii Warroomii g itti hojii irra oolchi, g(x) argadhu.</li> <li>Bu’aa g(x) fudhadhuutii Warroomii f irratti hojii irra oolchi, f(g(x)) argadhu.</li></ol> <p>Warroomiin bu’aa f(g(x)) walseennoo f fi g bakka bu’a, bakka bu’aan g akka galtee f tajaajilu. </p><p><b>Fakkii</b>: Fakkiin tuuta A Warroomii f jalatti, f(A) jedhamee kan agarsiifamu, tuuta elementoota hunda koodoomeenii keessa jiran (tuuta Warroomichi itti kaartaa godhu) kanneen yeroo galteen irraa dhufu firii Warroomichaa ta'aniidha saagi A. Jecha biraatiin, fakkiin tuuta gatiiwwan ta'uu danda'an hunda kan Warroomichi yeroo galteen tuuta A irraa filatamu oomishuu danda'uudha. </p><p>Fakkeenyaaf, yoo Warroomii f qabaanne: X -> Y, fi A citatuuta X ta’e, fakkiin A f jalatti, akka f(A)tti agarsiifame, tuuta elementoota hunda y Y keessatti akka achitti A keessatti x kan f(x) = y ta’eef jira. </p><p><b>Fakkii duraa:</b> Fakkiin duraa tuuta B Warroomii f jalatti, f^(-1)(B) jedhamee kan agarsiifamu, tuuta elementoota hunda domeenii keessa jiran (tuutaa Warroomichi irraa kaartaa godhu) kan, yeroo Warroomicha keessatti cufamu , firii kan tuuta B ta’e ni uumu.Jecha biraatiin, fakkiin duraa tuuta galteewwan ta’uu danda’an hunda kan firii tuuta B keessatti argamsiisudha. </p><p>Fakkeenyaaf, yoo Warroomii<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\rightarrow Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:X\rightarrow Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b215af1e965d0595a97ad2b21f7d0cbcf6281303" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.583ex; height:2.509ex;" alt="{\displaystyle f:X\rightarrow Y}"></span> qabaanne, fi B cita tuuta Y ta’e, fakkiin duraa B f jalatti, f^(-1)(B) jedhamee kan agarsiifamu, tuuta elementoota hunda x ti X keessatti akka f(x) kan B ta’u. </p> <div class="mw-heading mw-heading3"><h3 id="Warroomii_Tokko_tokkof,_Warroomii_tokko_tokkof_gitaa,_warroomii_irratti"><span id="Warroomii_Tokko_tokkof.2C_Warroomii_tokko_tokkof_gitaa.2C_warroomii_irratti"></span>Warroomii Tokko tokkof, Warroomii tokko tokkof gitaa, warroomii irratti</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=11" title="Kutaa gulaali: Warroomii Tokko tokkof, Warroomii tokko tokkof gitaa, warroomii irratti" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=11" title="Edit section's source code: Warroomii Tokko tokkof, Warroomii tokko tokkof gitaa, warroomii irratti"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Warroomii_Tokko_tokkof_(one_to_one_function)"><span id="Warroomii_Tokko_tokkof_.28one_to_one_function.29"></span>Warroomii Tokko tokkof (one to one function)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=12" title="Kutaa gulaali: Warroomii Tokko tokkof (one to one function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=12" title="Edit section's source code: Warroomii Tokko tokkof (one to one function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mee <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:A\rightarrow B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\rightarrow B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2fb4d5e9d282ee5442719053c46ad1ad96f2ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.509ex;" alt="{\displaystyle f:A\rightarrow B}"></span> Warroomiidha haa jennuu. f Warroomii tokko tokkof kan jennuu yoo<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(y)\Rightarrow x=y\Rightarrow ykn\Rightarrow x\neq y\Rightarrow f(x)=f(y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">⇒</mo> <mi>x</mi> <mo>=</mo> <mi>y</mi> <mo stretchy="false">⇒</mo> <mi>y</mi> <mi>k</mi> <mi>n</mi> <mo stretchy="false">⇒</mo> <mi>x</mi> <mo>≠</mo> <mi>y</mi> <mo stretchy="false">⇒</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=f(y)\Rightarrow x=y\Rightarrow ykn\Rightarrow x\neq y\Rightarrow f(x)=f(y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04a4f0bfe2d705672b786a1647e5e8df97665d30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.904ex; height:2.843ex;" alt="{\displaystyle f(x)=f(y)\Rightarrow x=y\Rightarrow ykn\Rightarrow x\neq y\Rightarrow f(x)=f(y)}"></span> ta'e dha. fknf f(x) - 4x -6 </p> <div class="mw-heading mw-heading4"><h4 id="Warroomii_irratti_(on_to_function)"><span id="Warroomii_irratti_.28on_to_function.29"></span>Warroomii irratti (on to function)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=13" title="Kutaa gulaali: Warroomii irratti (on to function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=13" title="Edit section's source code: Warroomii irratti (on to function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mee <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:A\rightarrow B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\rightarrow B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2fb4d5e9d282ee5442719053c46ad1ad96f2ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.509ex;" alt="{\displaystyle f:A\rightarrow B}"></span> Warroomiidha haa jennuu. f Warroomii irrattiiti kan jennuu yoo hangiin f=B ykn <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 y\in B,\exists x\in A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>y</mi> <mo>∈</mo> <mi>B</mi> <mo>,</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo>∈</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall y\in B,\exists x\in A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fae2b0c8a297422caab5b69a0882f1c9772e6c10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.293ex; height:2.509ex;" alt="{\displaystyle \forall y\in B,\exists x\in A}"></span> akka f(x)= y ta;uutti yoo ta'edha. </p> <div class="mw-heading mw-heading4"><h4 id="Warroomii_tokko_tokkof_gitaa(one_to_one_corresponde_function)"><span id="Warroomii_tokko_tokkof_gitaa.28one_to_one_corresponde_function.29"></span>Warroomii tokko tokkof gitaa(one to one corresponde function)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Warroomii_(faankishinii)&veaction=edit&section=14" title="Kutaa gulaali: Warroomii tokko tokkof gitaa(one to one corresponde function)" class="mw-editsection-visualeditor"><span>gulaali</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Warroomii_(faankishinii)&action=edit&section=14" title="Edit section's source code: Warroomii tokko tokkof gitaa(one to one corresponde function)"><span>lakkaddaa gulaali</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mee <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:A\rightarrow B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:A\rightarrow B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa2fb4d5e9d282ee5442719053c46ad1ad96f2ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.337ex; height:2.509ex;" alt="{\displaystyle f:A\rightarrow B}"></span> Warroomiidha haa jennuu. f Warroomii tokko tokkof gitaati kan jennuu yoo f Warroomii tokko tokkof fi Warroomii irratti yoo ta'eedha. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">"<a dir="ltr" href="https://om.wikipedia.org/w/index.php?title=Warroomii_(faankishinii)&oldid=42150">https://om.wikipedia.org/w/index.php?title=Warroomii_(faankishinii)&oldid=42150</a>" irraa kan fudhatame</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Ramaddii</a>: <ul><li><a href="/wiki/Category:Herreega" title="Category:Herreega">Herreega</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Fuulli kun dhumarratti kan gulaalame guyyaa 8 Amajjii 2024, sa'aa 19:08 irratti.</li> <li id="footer-info-copyright">Barreeffamichi kan argamu <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Eeyyama amala waliiqoodu wantootaa</a> jalatti; 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