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class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="İçindekiler" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div 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">İçindekiler</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">kenar çubuğuna taşı</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">gizle</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">Giriş</div> </a> </li> <li id="toc-Ters_fonksiyon_bulma" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ters_fonksiyon_bulma"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Ters fonksiyon bulma</span> </div> </a> <ul id="toc-Ters_fonksiyon_bulma-sublist" class="vector-toc-list"> </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="İçindekiler" 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="İçindekiler tablosunu değiştir" > <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">İçindekiler tablosunu değiştir</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">Ters fonksiyon</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="Başka bir dildeki sayfaya gidin. 61 dilde mevcut" > <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-61" 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">61 dil</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%98%E1%88%8B%E1%88%BD_%E1%8A%A0%E1%88%B5%E1%88%A8%E1%8A%AB%E1%89%A2" title="መላሽ አስረካቢ - Amharca" lang="am" hreflang="am" data-title="መላሽ አስረካቢ" data-language-autonym="አማርኛ" data-language-local-name="Amharca" class="interlanguage-link-target"><span>አማርኛ</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_%D8%B9%D9%83%D8%B3%D9%8A%D8%A9" title="دالة عكسية - Arapça" lang="ar" hreflang="ar" data-title="دالة عكسية" data-language-autonym="العربية" data-language-local-name="Arapça" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/T%C9%99rs_funksiya" title="Tərs funksiya - Azerbaycan dili" lang="az" hreflang="az" data-title="Tərs funksiya" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaycan dili" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B4%D0%B2%D0%B0%D1%80%D0%BE%D1%82%D0%BD%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F" title="Адваротная функцыя - Belarusça" lang="be" hreflang="be" data-title="Адваротная функцыя" data-language-autonym="Беларуская" data-language-local-name="Belarusça" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%B0%D1%82%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Обратна функция - Bulgarca" lang="bg" hreflang="bg" data-title="Обратна функция" data-language-autonym="Български" data-language-local-name="Bulgarca" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Inverzna_funkcija" title="Inverzna funkcija - Boşnakça" lang="bs" hreflang="bs" data-title="Inverzna funkcija" data-language-autonym="Bosanski" data-language-local-name="Boşnakça" 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_inversa" title="Funció inversa - Katalanca" lang="ca" hreflang="ca" data-title="Funció inversa" data-language-autonym="Català" data-language-local-name="Katalanca" 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%DB%8C_%DA%BE%DB%95%DA%B5%DA%AF%DB%95%DA%95%D8%A7%D9%88%DB%95" title="فانکشنی ھەڵگەڕاوە - Orta Kürtçe" lang="ckb" hreflang="ckb" data-title="فانکشنی ھەڵگەڕاوە" data-language-autonym="کوردی" data-language-local-name="Orta Kürtçe" 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/Inverzn%C3%AD_zobrazen%C3%AD" title="Inverzní zobrazení - Çekçe" lang="cs" hreflang="cs" data-title="Inverzní zobrazení" data-language-autonym="Čeština" data-language-local-name="Çekçe" 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%9A%D1%83%D1%82%C4%83%D0%BD%D0%BB%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8" title="Кутăнла функци - Çuvaşça" lang="cv" hreflang="cv" data-title="Кутăнла функци" data-language-autonym="Чӑвашла" data-language-local-name="Çuvaşça" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Invers_funktion" title="Invers funktion - Danca" lang="da" hreflang="da" data-title="Invers funktion" data-language-autonym="Dansk" data-language-local-name="Danca" 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/Umkehrfunktion" title="Umkehrfunktion - Almanca" lang="de" hreflang="de" data-title="Umkehrfunktion" data-language-autonym="Deutsch" data-language-local-name="Almanca" 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%91%CE%BD%CF%84%CE%AF%CF%83%CF%84%CF%81%CE%BF%CF%86%CE%B7_%CF%83%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7" title="Αντίστροφη συνάρτηση - Yunanca" lang="el" hreflang="el" data-title="Αντίστροφη συνάρτηση" data-language-autonym="Ελληνικά" data-language-local-name="Yunanca" 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/Inverse_function" title="Inverse function - İngilizce" lang="en" hreflang="en" data-title="Inverse function" data-language-autonym="English" data-language-local-name="İngilizce" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Funci%C3%B3n_inversa" title="Función inversa - İspanyolca" lang="es" hreflang="es" data-title="Función inversa" data-language-autonym="Español" data-language-local-name="İspanyolca" 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/P%C3%B6%C3%B6rdfunktsioon" title="Pöördfunktsioon - Estonca" lang="et" hreflang="et" data-title="Pöördfunktsioon" data-language-autonym="Eesti" data-language-local-name="Estonca" 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/Alderantzizko_funtzio" title="Alderantzizko funtzio - Baskça" lang="eu" hreflang="eu" data-title="Alderantzizko funtzio" data-language-autonym="Euskara" data-language-local-name="Baskça" 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_%D9%88%D8%A7%D8%B1%D9%88%D9%86" title="تابع وارون - Farsça" lang="fa" hreflang="fa" data-title="تابع وارون" data-language-autonym="فارسی" data-language-local-name="Farsça" 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/K%C3%A4%C3%A4nteisfunktio" title="Käänteisfunktio - Fince" lang="fi" hreflang="fi" data-title="Käänteisfunktio" data-language-autonym="Suomi" data-language-local-name="Fince" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Bijection_r%C3%A9ciproque" title="Bijection réciproque - Fransızca" lang="fr" hreflang="fr" data-title="Bijection réciproque" data-language-autonym="Français" data-language-local-name="Fransızca" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Funci%C3%B3n_inversa" title="Función inversa - Galiçyaca" lang="gl" hreflang="gl" data-title="Función inversa" data-language-autonym="Galego" data-language-local-name="Galiçyaca" 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_%D7%94%D7%A4%D7%99%D7%9B%D7%94" title="פונקציה הפיכה - İbranice" lang="he" hreflang="he" data-title="פונקציה הפיכה" data-language-autonym="עברית" data-language-local-name="İbranice" 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%AA%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BF%E0%A4%B2%E0%A5%8B%E0%A4%AE_%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="प्रतिलोम फलन - Hintçe" lang="hi" hreflang="hi" data-title="प्रतिलोम फलन" data-language-autonym="हिन्दी" data-language-local-name="Hintçe" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Inverzna_funkcija" title="Inverzna funkcija - Hırvatça" lang="hr" hreflang="hr" data-title="Inverzna funkcija" data-language-autonym="Hrvatski" data-language-local-name="Hırvatça" 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/Inverz_f%C3%BCggv%C3%A9ny" title="Inverz függvény - Macarca" lang="hu" hreflang="hu" data-title="Inverz függvény" data-language-autonym="Magyar" data-language-local-name="Macarca" 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%80%D5%A1%D5%AF%D5%A1%D5%A4%D5%A1%D6%80%D5%B1_%D6%86%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1" title="Հակադարձ ֆունկցիա - Ermenice" lang="hy" hreflang="hy" data-title="Հակադարձ ֆունկցիա" data-language-autonym="Հայերեն" data-language-local-name="Ermenice" 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_inverse" title="Function inverse - İnterlingua" lang="ia" hreflang="ia" data-title="Function inverse" data-language-autonym="İnterlingua" data-language-local-name="İnterlingua" class="interlanguage-link-target"><span>İnterlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Fungsi_invers" title="Fungsi invers - Endonezce" lang="id" hreflang="id" data-title="Fungsi invers" data-language-autonym="Bahasa Indonesia" data-language-local-name="Endonezce" 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/Simetra_elemento" title="Simetra elemento - Ido" lang="io" hreflang="io" data-title="Simetra elemento" 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/Andhverfa" title="Andhverfa - İzlandaca" lang="is" hreflang="is" data-title="Andhverfa" data-language-autonym="Íslenska" data-language-local-name="İzlandaca" 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_inversa" title="Funzione inversa - İtalyanca" lang="it" hreflang="it" data-title="Funzione inversa" data-language-autonym="İtaliano" data-language-local-name="İtalyanca" class="interlanguage-link-target"><span>İtaliano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%80%86%E5%86%99%E5%83%8F" title="逆写像 - Japonca" lang="ja" hreflang="ja" data-title="逆写像" data-language-autonym="日本語" data-language-local-name="Japonca" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B5%D1%80%D1%96_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Кері функция - Kazakça" lang="kk" hreflang="kk" data-title="Кері функция" data-language-autonym="Қазақша" data-language-local-name="Kazakça" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B3%8D%E0%B2%AF%E0%B2%B8%E0%B3%8D%E0%B2%A4_%E0%B2%AB%E0%B2%B2%E0%B2%A8" title="ವ್ಯಸ್ತ ಫಲನ - Kannada dili" lang="kn" hreflang="kn" data-title="ವ್ಯಸ್ತ ಫಲನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada dili" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%AD%ED%95%A8%EC%88%98" title="역함수 - Korece" lang="ko" hreflang="ko" data-title="역함수" data-language-autonym="한국어" data-language-local-name="Korece" 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_inversa" title="Functio inversa - Latince" lang="la" hreflang="la" data-title="Functio inversa" data-language-autonym="Latina" data-language-local-name="Latince" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Aplicaziun_recipruca" title="Aplicaziun recipruca - Lombardça" lang="lmo" hreflang="lmo" data-title="Aplicaziun recipruca" data-language-autonym="Lombard" data-language-local-name="Lombardça" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D0%B2%D0%B5%D1%80%D0%B7%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Инверзна функција - Makedonca" lang="mk" hreflang="mk" data-title="Инверзна функција" data-language-autonym="Македонски" data-language-local-name="Makedonca" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Fungsi_songsang" title="Fungsi songsang - Malayca" lang="ms" hreflang="ms" data-title="Fungsi songsang" data-language-autonym="Bahasa Melayu" data-language-local-name="Malayca" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%AA%E0%A4%B0%E0%A5%80%E0%A4%A4_%E0%A4%AB%E0%A4%B2%E0%A4%A8" title="विपरीत फलन - Nepalce" lang="ne" hreflang="ne" data-title="विपरीत फलन" data-language-autonym="नेपाली" data-language-local-name="Nepalce" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Inverteerbaar" title="Inverteerbaar - Felemenkçe" lang="nl" hreflang="nl" data-title="Inverteerbaar" data-language-autonym="Nederlands" data-language-local-name="Felemenkçe" 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/Invers_funksjon" title="Invers funksjon - Norveççe Nynorsk" lang="nn" hreflang="nn" data-title="Invers funksjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveççe Nynorsk" 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/Invers_funksjon" title="Invers funksjon - Norveççe Bokmål" lang="nb" hreflang="nb" data-title="Invers funksjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norveççe Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funkcja_odwrotna" title="Funkcja odwrotna - Lehçe" lang="pl" hreflang="pl" data-title="Funkcja odwrotna" data-language-autonym="Polski" data-language-local-name="Lehçe" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_inversa" title="Função inversa - Portekizce" lang="pt" hreflang="pt" data-title="Função inversa" data-language-autonym="Português" data-language-local-name="Portekizce" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Func%C8%9Bie_invers%C4%83" title="Funcție inversă - Rumence" lang="ro" hreflang="ro" data-title="Funcție inversă" data-language-autonym="Română" data-language-local-name="Rumence" 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%9E%D0%B1%D1%80%D0%B0%D1%82%D0%BD%D0%B0%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Обратная функция - Rusça" lang="ru" hreflang="ru" data-title="Обратная функция" data-language-autonym="Русский" data-language-local-name="Rusça" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Inverse_function" title="Inverse function - Simple English" lang="en-simple" hreflang="en-simple" data-title="Inverse function" 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/Inverzn%C3%A9_zobrazenie_(funkcia)" title="Inverzné zobrazenie (funkcia) - Slovakça" lang="sk" hreflang="sk" data-title="Inverzné zobrazenie (funkcia)" data-language-autonym="Slovenčina" data-language-local-name="Slovakça" 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/Inverzna_funkcija" title="Inverzna funkcija - Slovence" lang="sl" hreflang="sl" data-title="Inverzna funkcija" data-language-autonym="Slovenščina" data-language-local-name="Slovence" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Funksioni_i_anasjellt%C3%AB" title="Funksioni i anasjelltë - Arnavutça" lang="sq" hreflang="sq" data-title="Funksioni i anasjelltë" data-language-autonym="Shqip" data-language-local-name="Arnavutça" 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%98%D0%BD%D0%B2%D0%B5%D1%80%D0%B7%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Инверзна функција - Sırpça" lang="sr" hreflang="sr" data-title="Инверзна функција" data-language-autonym="Српски / srpski" data-language-local-name="Sırpça" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Invers_funktion" title="Invers funktion - İsveççe" lang="sv" hreflang="sv" data-title="Invers funktion" data-language-autonym="Svenska" data-language-local-name="İsveççe" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%81%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81" title="நேர்மாறுச் சார்பு - Tamilce" lang="ta" hreflang="ta" data-title="நேர்மாறுச் சார்பு" data-language-autonym="தமிழ்" data-language-local-name="Tamilce" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Inbersong_punsiyon" title="Inbersong punsiyon - Tagalogca" lang="tl" hreflang="tl" data-title="Inbersong punsiyon" data-language-autonym="Tagalog" data-language-local-name="Tagalogca" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D0%B5%D1%80%D0%BD%D0%B5%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%8F" title="Обернена функція - Ukraynaca" lang="uk" hreflang="uk" data-title="Обернена функція" data-language-autonym="Українська" data-language-local-name="Ukraynaca" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%A0m_ng%C6%B0%E1%BB%A3c" title="Hàm ngược - Vietnamca" lang="vi" hreflang="vi" data-title="Hàm ngược" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamca" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8F%8D%E5%87%BD%E6%95%B0" title="反函数 - Wu Çincesi" lang="wuu" hreflang="wuu" data-title="反函数" data-language-autonym="吴语" data-language-local-name="Wu Çincesi" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%87%BD%E6%95%B8" title="反函數 - Çince" lang="zh" hreflang="zh" data-title="反函數" data-language-autonym="中文" data-language-local-name="Çince" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ge%CC%8Dk-h%C3%A2m-s%C3%B2%CD%98" title="Ge̍k-hâm-sò͘ - Min Nan Çincesi" lang="nan" hreflang="nan" data-title="Ge̍k-hâm-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Min Nan Çincesi" 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%8F%8D%E5%87%BD%E6%95%B8" title="反函數 - Kantonca" lang="yue" hreflang="yue" data-title="反函數" data-language-autonym="粵語" data-language-local-name="Kantonca" 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/Q191884#sitelinks-wikipedia" title="Dillerarası bağlantıları değiştir" class="wbc-editpage">Bağlantıları değiştir</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="Ad alanları"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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mw-parser-output" lang="tr" dir="ltr"><table class="box-Kaynaksız plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Dosya:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Bu madde <b>hiçbir <a href="/wiki/Vikipedi:Kaynak_g%C3%B6sterme" title="Vikipedi:Kaynak gösterme">kaynak</a> <a href="/wiki/Vikipedi:Do%C4%9Frulanabilirlik" title="Vikipedi:Doğrulanabilirlik">içermemektedir</a>.</b><span class="hide-when-compact"> Lütfen <a href="/wiki/Yard%C4%B1m:Dipnotlar" title="Yardım:Dipnotlar">güvenilir kaynaklar ekleyerek</a> <a class="external text" href="https://tr.wikipedia.org/w/index.php?title=Ters_fonksiyon&action=edit">madde içeriğinin geliştirilmesine</a> yardımcı olun. Kaynaksız içerik itiraz konusu olabilir ve <a href="/wiki/Vikipedi:Do%C4%9Frulanabilirlik#Kanıt_sorumluluğu" title="Vikipedi:Doğrulanabilirlik">kaldırılabilir</a>.<br /><small><span class="plainlinks"><i>Kaynak ara:</i> <a rel="nofollow" class="external text" href="//www.google.com/search?as_eq=wikipedia&q=%22Ters+fonksiyon%22">"Ters fonksiyon"</a> – <a rel="nofollow" class="external text" href="//www.google.com/search?tbm=nws&q=%22Ters+fonksiyon%22+-wikipedia">haber</a> · <a rel="nofollow" class="external text" href="//www.google.com/search?&q=%22Ters+fonksiyon%22+site:news.google.com/newspapers&source=newspapers">gazete</a> · <a rel="nofollow" class="external text" href="//www.google.com/search?tbs=bks:1&q=%22Ters+fonksiyon%22+-wikipedia">kitap</a> · <a rel="nofollow" class="external text" href="//scholar.google.com/scholar?q=%22Ters+fonksiyon%22">akademik</a> · <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Ters+fonksiyon%22&acc=on&wc=on">JSTOR</a></span></small></span> <small class="date-container"><i>(<span class="date">Şubat 2017</span>)</i></small><small class="hide-when-compact"><i> (<a href="/wiki/Yard%C4%B1m:Bak%C4%B1m_%C5%9Fablonunu_kald%C4%B1rmak" title="Yardım:Bakım şablonunu kaldırmak">Bu şablonun nasıl ve ne zaman kaldırılması gerektiğini öğrenin</a>)</i></small></div></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r33092931">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid #aaa;padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar nomobile"><tbody><tr><th class="sidebar-title" style="letter-spacing:0.0125em; background-color:#FFCC99"><a href="/wiki/Fonksiyon_(matematik)" class="mw-redirect" title="Fonksiyon (matematik)">Fonksiyon</a></th></tr><tr><td class="sidebar-image"><span style="font-size: 200%;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\to f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\to f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15b4bdec7eedd3f668d23f839b83adbe58c86908" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.361ex; height:2.843ex;" alt="{\displaystyle x\to f(x)}"></span></span></td></tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> <a href="/w/index.php?title=Fonksiyon_kavram%C4%B1n%C4%B1n_tarihi&action=edit&redlink=1" class="new" title="Fonksiyon kavramının tarihi (sayfa mevcut değil)">Fonksiyon kavramının tarihi</a></th></tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> <a href="/wiki/Tan%C4%B1m_k%C3%BCmesi" title="Tanım kümesi">Tanım</a> ve <a href="/wiki/De%C4%9Fer_k%C3%BCmesi" title="Değer kümesi">değer</a> kümelerine göre</th></tr><tr><td class="sidebar-content"> <style data-mw-deduplicate="TemplateStyles:r32637355">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"> <ul><li><a href="/w/index.php?title=Boolean-valued_function&action=edit&redlink=1" class="new" title="Boolean-valued function (sayfa mevcut değil)"><span class="texhtml"><span title="arbitrary set"><var>X</var></span> → <span title="Codomain of Booleans">𝔹</span></span></a></li> <li><a href="/w/index.php?title=Ordered_pair&action=edit&redlink=1" class="new" title="Ordered pair (sayfa mevcut değil)"> <span class="texhtml"><span title="Domain of Booleans">𝔹</span> → <span title="arbitrary set"><var>X</var></span></span></a></li> <li><a href="/w/index.php?title=Boolean_function&action=edit&redlink=1" class="new" title="Boolean function (sayfa mevcut değil)"> <span class="texhtml"><span title="several Boolean variables">𝔹<sup><var>n</var></sup></span> → <span title="Codomain of natural numbers"><var>X</var></span></span></a></li> <li><a href="/w/index.php?title=%C4%B0nteger-valued_function&action=edit&redlink=1" class="new" title="İnteger-valued function (sayfa mevcut değil)"> <span class="texhtml"><span title="arbitrary set"><var>X</var></span> → <span title="integers">ℤ</span></span></a></li> <li><a href="/wiki/Dizi" title="Dizi"> <span class="texhtml"><span title="integers">ℤ</span> → <span title="arbitrary set"><var>X</var></span></span></a></li> <li><a href="/wiki/Ger%C3%A7el_fonksiyon" title="Gerçel fonksiyon"> <span class="texhtml"><span title="arbitrary set"><var>X</var></span> → <span title="real numbers">ℝ</span></span></a></li> <li><a href="/w/index.php?title=Function_of_a_real_variable&action=edit&redlink=1" class="new" title="Function of a real variable (sayfa mevcut değil)"> <span class="texhtml"><span title="real numbers">ℝ</span> → <span title="arbitrary set"><var>X</var></span></span></a></li> <li><a href="/w/index.php?title=Function_of_several_real_variables&action=edit&redlink=1" class="new" title="Function of several real variables (sayfa mevcut değil)"> <span class="texhtml"><span title="real coordinate (or Euclidean) space">ℝ<sup><var>n</var></sup></span> → <span title="arbitrary set"><var>X</var></span></span></a></li> <li><a href="/w/index.php?title=Complex-valued_function&action=edit&redlink=1" class="new" title="Complex-valued function (sayfa mevcut değil)"> <span class="texhtml"><span title="arbitrary set"><var>X</var></span> → <span title="complex numbers">ℂ</span></span></a></li> <li><a href="/wiki/Karma%C5%9F%C4%B1k_analiz" title="Karmaşık analiz"> <span class="texhtml"><span title="complex numbers">ℂ</span> → <span title="arbitrary set"><var>X</var></span></span></a></li> <li><a href="/w/index.php?title=Function_of_several_complex_variables&action=edit&redlink=1" class="new" title="Function of several complex variables (sayfa mevcut değil)"> <span class="texhtml"><span title="complex coordinate space">ℂ<sup><var>n</var></sup></span> → <span title="arbitrary set"><var>X</var></span></span></a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> <a href="/w/index.php?title=List_of_types_of_functions&action=edit&redlink=1" class="new" title="List of types of functions (sayfa mevcut değil)">Sınıflarına/özelliklerine göre</a> </th></tr><tr><td class="sidebar-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r32637355"><div class="hlist"> <ul><li><a href="/wiki/Sabit_fonksiyon" title="Sabit fonksiyon">Sabit</a></li> <li><a href="/wiki/Birim_fonksiyon" title="Birim fonksiyon">Birim</a></li> <li><a href="/wiki/Do%C4%9Frusal_d%C3%B6n%C3%BC%C5%9F%C3%BCm" title="Doğrusal dönüşüm">Lineer</a></li> <li><a href="/wiki/Polinom" title="Polinom">Polinomyal</a></li> <li><a href="/w/index.php?title=Rational_function&action=edit&redlink=1" class="new" title="Rational function (sayfa mevcut değil)">Rasyonel</a></li> <li><a href="/w/index.php?title=Algebraic_function&action=edit&redlink=1" class="new" title="Algebraic function (sayfa mevcut değil)">Cebir</a></li> <li><a href="/wiki/Analitik_fonksiyon" title="Analitik fonksiyon">Analitik</a></li> <li><a href="/wiki/D%C3%BCzg%C3%BCnl%C3%BCk" title="Düzgünlük">Düzgün</a></li> <li><a href="/wiki/S%C3%BCreklilik" title="Süreklilik">Sürekli</a></li> <li><a href="/w/index.php?title=Measurable_function&action=edit&redlink=1" class="new" title="Measurable function (sayfa mevcut değil)">Ölçülebilir</a></li> <li><a href="/wiki/Birebir_fonksiyon" title="Birebir fonksiyon">Birebir</a></li> <li><a href="/wiki/%C3%96rten_fonksiyon" title="Örten fonksiyon">Örten</a></li> <li><a href="/wiki/Birebir_%C3%B6rten_fonksiyon" title="Birebir örten fonksiyon">Birebir örten</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> Yapılarına göre</th></tr><tr><td class="sidebar-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r32637355"><div class="hlist"> <ul><li><a href="/w/index.php?title=Restriction_(mathematics)&action=edit&redlink=1" class="new" title="Restriction (mathematics) (sayfa mevcut değil)">Restriction</a></li> <li><a href="/wiki/Bile%C5%9Fke_fonksiyon" title="Bileşke fonksiyon">Birleşim</a></li> <li><a href="/wiki/Lamda_kalk%C3%BCl%C3%BCs" title="Lamda kalkülüs">λ</a></li> <li><a class="mw-selflink selflink">Ters</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> Genellemelere göre </th></tr><tr><td class="sidebar-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r32637355"><div class="hlist"> <ul><li><a href="/w/index.php?title=Binary_relation&action=edit&redlink=1" class="new" title="Binary relation (sayfa mevcut değil)">Binary relation</a></li> <li><a href="/wiki/Par%C3%A7al%C4%B1_fonksiyon" title="Parçalı fonksiyon">Parçalı</a></li> <li><a href="/wiki/%C3%87okde%C4%9Ferli_fonksiyon" title="Çokdeğerli fonksiyon">Çokdeğerli</a></li> <li><a href="/w/index.php?title=Implicit_function&action=edit&redlink=1" class="new" title="Implicit function (sayfa mevcut değil)">Implicit</a></li> <li><a href="/w/index.php?title=Function_space&action=edit&redlink=1" class="new" title="Function space (sayfa mevcut değil)">Space</a></li> <li><a href="/w/index.php?title=Higher-order_function&action=edit&redlink=1" class="new" title="Higher-order function (sayfa mevcut değil)">Higher-order</a></li> <li><a href="/w/index.php?title=Morphism&action=edit&redlink=1" class="new" title="Morphism (sayfa mevcut değil)">Morphism</a></li> <li><a href="/w/index.php?title=Functor&action=edit&redlink=1" class="new" title="Functor (sayfa mevcut değil)">Functor</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-size: 117%; letter-spacing: 0.0125em; font-weight: 500; border-top: 1px solid black; padding: 5px 0 3px"> <a href="/wiki/Matematiksel_fonksiyonlar%C4%B1n_listesi" title="Matematiksel fonksiyonların listesi">Özel fonksiyonların listesi</a></th></tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r25548259">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="plainlinks hlist navbar navbar-mini"><ul><li class="nv-view"><a href="/w/index.php?title=%C5%9Eablon:Functions&action=edit&redlink=1" class="new" title="Şablon:Functions (sayfa mevcut değil)"><abbr title="Bu şablonu görüntüle">g</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=%C5%9Eablon_tart%C4%B1%C5%9Fma:Functions&action=edit&redlink=1" class="new" title="Şablon tartışma:Functions (sayfa mevcut değil)"><abbr title="Bu şablonu tartış">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://tr.wikipedia.org/w/index.php?title=%C5%9Eablon:Functions&action=edit"><abbr title="Bu şablonu değiştir">d</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Inverse_Function.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Inverse_Function.png/220px-Inverse_Function.png" decoding="async" width="220" height="337" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Inverse_Function.png/330px-Inverse_Function.png 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c8/Inverse_Function.png 2x" data-file-width="336" data-file-height="515" /></a><figcaption>A fonksiyonu ƒ ve tersi ƒ<sup>–1</sup>. Çünkü ƒ <i>a</i> yı 3'e götürür, tersi ƒ<sup>–1</sup> 3'ü <i>a</i> ya götürür.</figcaption></figure> <p>Matematikte <b>ters fonksiyon</b>, bir <a href="/wiki/Fonksiyon" title="Fonksiyon">fonksiyonun</a> görüntü kümesinden alınan herhangi bir elemanını tanım kümesindeki aslına gönderen fonksiyona denir. Bir fonksiyonun tersi, fonksiyon <a href="/wiki/Birebir_fonksiyon" title="Birebir fonksiyon">birebir</a> ve <a href="/wiki/%C3%96rten_fonksiyon" title="Örten fonksiyon">örten</a> ise tanımlı olabilir. Ters fonksiyon <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^{-1}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46a543a3462cbb9effd5d0c514529426172c7d7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.792ex; height:3.176ex;" alt="{\displaystyle f^{-1}(x)}"></span> ile gösterilir. Ancak <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^{-1}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46a543a3462cbb9effd5d0c514529426172c7d7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.792ex; height:3.176ex;" alt="{\displaystyle f^{-1}(x)}"></span> yalnızca bir gösterim olup, "f(x) fonksiyonunun çarpmaya göre tersi" ile karıştırılmamalıdır. </p> <div class="mw-heading mw-heading2"><h2 id="Ters_fonksiyon_bulma">Ters fonksiyon bulma</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ters_fonksiyon&veaction=edit&section=1" title="Değiştirilen bölüm: Ters fonksiyon bulma" class="mw-editsection-visualeditor"><span>değiştir</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Ters_fonksiyon&action=edit&section=1" title="Bölümün kaynak kodunu değiştir: Ters fonksiyon bulma"><span>kaynağı değiştir</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Dosya:Inverse_Functions_Domain_and_Range.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Inverse_Functions_Domain_and_Range.png/240px-Inverse_Functions_Domain_and_Range.png" decoding="async" width="240" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/9d/Inverse_Functions_Domain_and_Range.png 1.5x" data-file-width="360" data-file-height="180" /></a><figcaption>Eğer ƒ <i>X</i> i <i>Y</i> ye götürüyorsa, ƒ<sup>–1</sup> <i>Y</i> yi <i>X</i> e götürür. Yani f(x) = y ise f<sup>-1</sup>(y) = x olur.</figcaption></figure> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=ax+b}"> <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>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=ax+b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75c655df4be41082c4bba924beab2c1dc27d019c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.913ex; height:2.843ex;" alt="{\displaystyle f(x)=ax+b}"></span> şeklindeki doğrusal fonksiyonların tersi <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^{-1}(x)={\cfrac {x-b}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>−</mo> <mi>b</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}(x)={\cfrac {x-b}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/adb045987364d1472086f14181234f115ac3403b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:15.894ex; height:7.176ex;" alt="{\displaystyle f^{-1}(x)={\cfrac {x-b}{a}}}"></span> dır.</li></ul> <dl><dd><dl><dd>Örnek: <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)=3x-2\Rightarrow f^{-1}(x)=f^{-1}(x)={\cfrac {x+2}{3}}}"> <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> <mn>3</mn> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">⇒</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>+</mo> <mn>2</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=3x-2\Rightarrow f^{-1}(x)=f^{-1}(x)={\cfrac {x+2}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2eea5bd6eb841b5f9097be6f34671bcc6046397c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:43.575ex; height:7.176ex;" alt="{\displaystyle f(x)=3x-2\Rightarrow f^{-1}(x)=f^{-1}(x)={\cfrac {x+2}{3}}}"></span></dd></dl></dd></dl> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\cfrac {ax+b}{cx+d}}}"> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>x</mi> <mo>+</mo> <mi>d</mi> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\cfrac {ax+b}{cx+d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3173cd075673cf545bfa241c0d8e0420344feddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.75ex; height:7.176ex;" alt="{\displaystyle f(x)={\cfrac {ax+b}{cx+d}}}"></span> fonksiyonunun tersi <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^{-1}(x)={\cfrac {-dx+b}{cx-a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> <mi>x</mi> <mo>−</mo> <mi>a</mi> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}(x)={\cfrac {-dx+b}{cx-a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64c0477399bd227de643ef6b3e83235acf8e04d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.919ex; height:7.176ex;" alt="{\displaystyle f^{-1}(x)={\cfrac {-dx+b}{cx-a}}}"></span> dır. Bir başka deyişle paydaki x'li terim ile paydadaki sabit sayının hem yerleri hem işaretleri değişir.</li></ul> <dl><dd><dl><dd>Örnek:<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)={\cfrac {x+6}{2x-5}}\Rightarrow f^{-1}(x)={\cfrac {5x+6}{2x-1}}}"> <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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>+</mo> <mn>6</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>x</mi> <mo>−</mo> <mn>5</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> <mo stretchy="false">⇒</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> <mi>x</mi> <mo>+</mo> <mn>6</mn> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\cfrac {x+6}{2x-5}}\Rightarrow f^{-1}(x)={\cfrac {5x+6}{2x-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e791634c1028eb21132e5b6f54631eb8be1c680" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.683ex; height:7.176ex;" alt="{\displaystyle f(x)={\cfrac {x+6}{2x-5}}\Rightarrow f^{-1}(x)={\cfrac {5x+6}{2x-1}}}"></span></dd></dl></dd></dl> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=ax^{2}+bx+c}"> <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>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=ax^{2}+bx+c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66fca4dfe28e7b4a4a336578daaab18c87397073" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.145ex; height:3.176ex;" alt="{\displaystyle f(x)=ax^{2}+bx+c}"></span> gibi ikinci dereceden polinom şeklindeki fonksiyonların tersini bulmak için şu yol uygulanır;</li></ul> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:(3,\infty )\rightarrow (4,\infty )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>,</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:(3,\infty )\rightarrow (4,\infty )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff3c6ad3ffd96cc7182bf36510e1dff72ccafa06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.489ex; height:2.843ex;" alt="{\displaystyle f:(3,\infty )\rightarrow (4,\infty )}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{2}-6x+13}"> <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> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>6</mn> <mi>x</mi> <mo>+</mo> <mn>13</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{2}-6x+13}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/894242e9b7a61eba943cc56e1ff96b578138dd04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.398ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{2}-6x+13}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=x^{2}-6x+13}"> <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> <mo>−</mo> <mn>6</mn> <mi>x</mi> <mo>+</mo> <mn>13</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=x^{2}-6x+13}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71c67c15fb6e05bbfd25f21ef974004df523c46f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.136ex; height:3.009ex;" alt="{\displaystyle y=x^{2}-6x+13}"></span> <i>(Bu aşamadan sonra x yalnız bırakılmaya çalışılacak.)</i></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=(x^{2}-6x+9)+4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>6</mn> <mi>x</mi> <mo>+</mo> <mn>9</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=(x^{2}-6x+9)+4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c216b32937b2c53c82b67c8fff4e289351c4de54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.785ex; height:3.176ex;" alt="{\displaystyle y=(x^{2}-6x+9)+4}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=(x-3)^{2}+4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>3</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=(x-3)^{2}+4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e497145c1f2ed1885434eaf3f16a775e254d0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.453ex; height:3.176ex;" alt="{\displaystyle y=(x-3)^{2}+4}"></span> <i>(İfadenin bir kısmı tam kare hâline çevrildi)</i></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y-4=(x-3)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>−</mo> <mn>4</mn> <mo>=</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>3</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y-4=(x-3)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b99d490179de2fd283df6cd543e487eb888a7b0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.453ex; height:3.176ex;" alt="{\displaystyle y-4=(x-3)^{2}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {y-4}}={\sqrt {(x-3)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>y</mi> <mo>−</mo> <mn>4</mn> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>3</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {y-4}}={\sqrt {(x-3)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75b1fa8246e88995c35ddf9be6f3b73d95853c28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:21.1ex; height:4.843ex;" alt="{\displaystyle {\sqrt {y-4}}={\sqrt {(x-3)^{2}}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {y-4}}=|x-3|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>y</mi> <mo>−</mo> <mn>4</mn> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mo>−</mo> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {y-4}}=|x-3|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9bedc7a7e09959830367b2fa2134b796b93623a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:17.207ex; height:3.509ex;" alt="{\displaystyle {\sqrt {y-4}}=|x-3|}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {y-4}}=x-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>y</mi> <mo>−</mo> <mn>4</mn> </msqrt> </mrow> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {y-4}}=x-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24c2e3459f5695dc82812b25bbf18708e065d363" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.913ex; height:3.509ex;" alt="{\displaystyle {\sqrt {y-4}}=x-3}"></span> <i>(x, 3 ten büyük olduğu için mutlak değer içi pozitiftir.)</i></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=3+{\sqrt {y-4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>y</mi> <mo>−</mo> <mn>4</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=3+{\sqrt {y-4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deb013ca29cf63f332c2a8a27ecb7d79f1745bf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.913ex; height:3.509ex;" alt="{\displaystyle x=3+{\sqrt {y-4}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f^{-1}(x)=3+{\sqrt {x-4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>3</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>x</mi> <mo>−</mo> <mn>4</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f^{-1}(x)=3+{\sqrt {x-4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a68f26b21430a5c2bb74fc1f9c78ba2a48ec7e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.162ex; height:3.176ex;" alt="{\displaystyle f^{-1}(x)=3+{\sqrt {x-4}}}"></span></dd></dl></dd></dl> <div role="navigation" class="navbox" aria-labelledby="Matematiksel_fonksiyonlar" style="padding:3px"><table class="nowraplinks hlist collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r25548259"><div class="plainlinks hlist navbar navbar-mini"><ul><li class="nv-view"><a href="/wiki/%C5%9Eablon:Matematiksel_fonksiyonlar" title="Şablon:Matematiksel fonksiyonlar"><abbr title="Bu şablonu görüntüle" style=";;background:none 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fonksiyon</a></li> <li><a href="/wiki/Tek_ve_%C3%A7ift_fonksiyonlar#Tek_fonksiyon" title="Tek ve çift fonksiyonlar">Tek fonksiyon</a></li> <li><a href="/w/index.php?title=Alttoplamsal_fonksiyon&action=edit&redlink=1" class="new" title="Alttoplamsal fonksiyon (sayfa mevcut değil)">Alttoplamsal fonksiyon</a></li> <li><a href="/w/index.php?title=%C3%9Csttoplamsal_fonksiyon&action=edit&redlink=1" class="new" title="Üsttoplamsal fonksiyon (sayfa mevcut değil)">Üsttoplamsal fonksiyon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topolojiye göre</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/S%C3%BCrekli_fonksiyon" class="mw-redirect" title="Sürekli fonksiyon">Sürekli fonksiyon</a></li> <li><a href="/w/index.php?title=Hi%C3%A7bir_yerde_s%C3%BCrekli_fonksiyon&action=edit&redlink=1" class="new" title="Hiçbir yerde sürekli fonksiyon (sayfa mevcut değil)">Hiçbir yerde sürekli fonksiyon</a></li> <li><a href="/wiki/Homeomorfizma" title="Homeomorfizma">Homeomorfizma</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sıralamaya göre</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Monoton_fonksiyon&action=edit&redlink=1" class="new" title="Monoton fonksiyon (sayfa mevcut değil)">Monoton fonksiyon</a></li> <li><a href="/w/index.php?title=S%C4%B1n%C4%B1rl%C4%B1_monoton_fonksiyon&action=edit&redlink=1" class="new" title="Sınırlı monoton fonksiyon (sayfa mevcut değil)">Sınırlı monoton fonksiyon</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Gerçel/Karmaşık sayılara göre</th><td class="navbox-list navbox-odd" 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