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hazırlanan öğrenciler ekran başına! Hız Yayınları Matematik Lise Yayın Yönetmenimiz Mustafa Güler, siz sevgili öğrencilerimiz için soru çözmeye devam ediyor. Bu videomuzda sizlerle...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3413672/493668ed662d0fc1db5edf4a1b86488c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/eHkRRAIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=videoid:16673635893251709415","teaser":[{"list":{"type":"unordered","items":["Bu video, Hız Yayınları matematik yayın yönetmeni Mustafa Güler'in AYT trigonometri sorusu çözdüğü bir eğitim içeriğidir. Mustafa Güler, \"Matematiğin Güler Yüzü\" olarak tanıtılmaktadır.","Videoda trigonometri konusundan toplam-fark formülleri kullanılarak bir soru çözülmektedir. Mustafa Güler, tanjant a+b ve tanjant a-b formüllerini hatırlatarak, verilen geometrik şekil üzerinden tanjant alfa değerini bulma sürecini adım adım göstermektedir. Soru çözümü sırasında oran-orantı ve trigonometrik oranlar kullanılarak tanjant m ve tanjant k değerleri hesaplanarak, tanjant alfa'nın 6 olduğu sonucuna varılmaktadır. Video, Mart ayında başlayacak olan AYT 20 deneme kampının ilk altı konusunun çözümüyle devam edeceğini belirterek sona ermektedir."]},"endTime":543,"title":"AYT Trigonometri Soru Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"AYT Kampı ve Kitap Tanıtımı","list":{"type":"unordered","items":["Hız Yayınları Matematik Yayın Yönetmeni Mustafa Güler, AYT sorusu çözecek.","Mart ayında AYT 20 deneme kampı başlayacak ve ilk altı konunun olduğu video yayında olacak.","\"AYT Son 500 soru\" adlı kitap hem altılı denemesi hem de kendisi satın alınabilir."]},"beginTime":7,"endTime":56,"href":"/video/preview/16673635893251709415?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=7&ask_summarization=1"},{"index":1,"title":"Trigonometri Sorusu Çözümü","list":{"type":"unordered","items":["Trigonometri'den toplam fark formülleri sorusu çözülecek.","Tanjant a+b formülü: tan(a+b) = (tan a + tan b) / (1 - tan a × tan b)","Tanjant a-b formülü: tan(a-b) = (tan a - tan b) / (1 + tan a × tan b)"]},"beginTime":56,"endTime":158,"href":"/video/preview/16673635893251709415?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=56&ask_summarization=1"},{"index":2,"title":"Sorunun Analizi","list":{"type":"unordered","items":["Soruda iki iç açının toplamı kendisine komşu olmayan dış açıya eşittir.","Alfa açısı, m ve k açılarının toplamı olarak ifade edilir.","Tanjant alfa, tanjant (m+k) formülüyle hesaplanır."]},"beginTime":158,"endTime":234,"href":"/video/preview/16673635893251709415?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=158&ask_summarization=1"},{"index":3,"title":"Geometrik Çözüm","list":{"type":"unordered","items":["Soruda verilen geometrik şekle göre, her bir karecik 2 birim olarak alınır.","Toplam uzunluk 16 birim olarak hesaplanır.","Tanjant m = 1 ve tanjant k = 5/7 olarak 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Öğretmen, mutlak değer problemlerinin hem problemli hem de problemsiz çözüm yöntemlerini anlatmaktadır.","Videoda öncelikle mutlak değer ifadelerinin içindekiler birbirine benzerken kolay çözümleri gösterilmektedir. Ardından içindekiler birbirine benzemeyen mutlak değer problemlerinin uzun çözüm yöntemi adım adım anlatılmakta ve ardından bu problemlerin daha kısa ve pratik bir yöntemle nasıl çözülebileceği açıklanmaktadır. 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tyt fonksiyonlar, matematiğin güler yüzü fonksiyonlar, ayt fonksiyonlar, 2018 tyt fonksiyonlar, mustafa güler fonksiyonlar, tyt bileşke fonksiyonlar, tyt ters fonksiyonlar, tyt...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3509048/6780c8072177c7a4eb7f9b52787ac8c5/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/3W-YlwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=videoid:3468484602478176835","teaser":[{"list":{"type":"unordered","items":["Bu video, Matematik öğretmeni Mustafa Güler'in sunduğu \"Matematiğin Güler Yüzü\" adlı canlı yayın programıdır. Öğretmen, tahtada notlar alarak ve öğrencilere hitap ederek fonksiyonlar konusunu anlatmaktadır.","Videoda fonksiyonların tanımı, özellikleri ve çeşitli soru tipleri detaylı şekilde ele alınmaktadır. Öğretmen, fonksiyonların tanım kümesi, değer kümesi ve görüntü kümesi kavramlarını açıklamakta, f(x) fonksiyonlarında değer bulma tekniklerini göstermekte ve TYT-LYS sınavlarından örnek sorular çözmektedir. Ayrıca fonksiyon olup olmadığını belirleme yöntemleri, parçalı fonksiyonlar ve fonksiyonların grafiksel gösterimi de örneklerle anlatılmaktadır.","Öğretmen, videonun sonunda önümüzdeki hafta fonksiyon çeşitleri, ters fonksiyon, bileşke fonksiyon ve grafik konularını işleyeceğini belirtmektedir. Video, öğrencilerin fonksiyon konusunu kavramaları ve sınavlarda karşılaştıkları soruları çözebilmesi için adım adım çözüm yöntemlerini sunmaktadır."]},"endTime":3157,"title":"Matematik Dersi: Fonksiyonlar Konusu","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyonlar Konusuna Giriş","list":{"type":"unordered","items":["Matematik öğretmeni Mustafa Güler, \"Matematiğin Güler Yüzü\" programında fonksiyonlar konusunu ele alıyor.","Öğrencilerin talebi üzerine polinomlardan sonra fonksiyonlar konusu işlenecek.","Öncelikle polinomlar yardımıyla fonksiyon sorularının çözülebilirliği gösterilecek, sonra fonksiyonun tanımı verilecek."]},"beginTime":23,"endTime":61,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=23&ask_summarization=1"},{"index":1,"title":"Fonksiyonlarda Değer Bulma","list":{"type":"unordered","items":["Fonksiyonlarda değer bulma işlemi, polinomlarda yapılan işlemlere benzer şekilde yapılır.","Fonksiyon içindeki x yerine istenen değer yazılır ve hesaplamalar yapılır.","Örneğin f(x) fonksiyonunda f(-2) değeri bulunurken x yerine -2 yazılır ve sonuç hesaplanır."]},"beginTime":61,"endTime":86,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=61&ask_summarization=1"},{"index":2,"title":"Fonksiyonlarda Değişken Değerlendirme","list":{"type":"unordered","items":["Fonksiyonlarda f(5) gibi bir değer istendiğinde, fonksiyon içindeki ifadeyi 5'e eşit hale getirmek için x'e uygun değer yazılır.","Örneğin f(x²+1) = f(x+2) denklemi verildiğinde, f(5) değeri için x'e -2 yazılır.","Fonksiyonlarda iç içe geçmiş fonksiyonlar da bulunabilir ve bu durumda içteki fonksiyonun değeri dıştaki fonksiyonun değeriyle eşitlenir."]},"beginTime":86,"endTime":222,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=86&ask_summarization=1"},{"index":3,"title":"Fonksiyonlarda Değişken Değiştirme","list":{"type":"unordered","items":["Fonksiyonlarda değişken değiştirme işlemi yapılırken, içteki ifadeye uygun değerler yazılır.","Örneğin f(2x-1) ifadesinde x yerine 2x-1 yazılır ve hesaplamalar yapılır.","Fonksiyonlarda içteki ifadeye uygun değerler yazarak sorular çözülebilir."]},"beginTime":222,"endTime":371,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=222&ask_summarization=1"},{"index":4,"title":"Fonksiyonlarda Denklem Çözümü","list":{"type":"unordered","items":["Fonksiyonlarda denklem çözümleri yapılırken, içteki ifadeye uygun değerler bulunur.","Örneğin f(ax+b) = -a/b denklemi verildiğinde, x = -b/a olarak bulunur.","Fonksiyonlarda denklem çözümleri yaparken, içteki ifadeye uygun değerler bulunarak sorular çözülebilir."]},"beginTime":371,"endTime":535,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=371&ask_summarization=1"},{"index":5,"title":"Fonksiyonlarda Uyanık Düşünme","list":{"type":"unordered","items":["Fonksiyonlarda uyanık düşünmek önemlidir, örneğin f(x) = xf(x-1) + 3 fonksiyonunda f(3) değeri bulunurken x = 0 yazarak f(2) = 3 bulunur.","Bulunan değerler kullanılarak diğer değerler hesaplanabilir.","Fonksiyonlarda matematik bilen bir öğrenci her zaman uyanık olur ve soruları farklı yollarla çözebilir."]},"beginTime":535,"endTime":717,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=535&ask_summarization=1"},{"index":6,"title":"Fonksiyon Problemleri","list":{"type":"unordered","items":["Öğretmen, f(x) = (x-1)/(x+2) fonksiyonunda x'i bulma sorusunu çözüyor.","İçerideki ifadeyi dışarıdaki ifadeye benzeterek çözüm yapılıyor: (x-1)/(x+2) = 1/2, (x+2)/3 = x şeklinde.","Çözüm sonucunda x = 3/2 olarak bulunuyor."]},"beginTime":720,"endTime":846,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=720&ask_summarization=1"},{"index":7,"title":"Fonksiyon Karakteristik Özellik Sorusu","list":{"type":"unordered","items":["f(x²+2x) = x⁴+4x³+4x² fonksiyonunda f(5) değerini bulma sorusu çözülüyor.","İçerideki ifade dışarıdakinin karesi olduğu görülüyor: (x²+2x)² = x⁴+4x³+4x².","f(5) = 5² = 25 olarak bulunuyor."]},"beginTime":846,"endTime":958,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=846&ask_summarization=1"},{"index":8,"title":"Fonksiyon Dizisi Sorusu","list":{"type":"unordered","items":["f(x+1) = x + f(x) fonksiyonunda f(40) değerini bulma sorusu çözülüyor.","f(x+1) - f(x) = x şeklinde yazarak, x = 1'den 39'a kadar değerleri topluyoruz.","f(40) - f(1) = 1+2+...+39 = 39×40/2 = 780 olarak bulunuyor."]},"beginTime":958,"endTime":1235,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=958&ask_summarization=1"},{"index":9,"title":"Parçalı Fonksiyon Sorusu","list":{"type":"unordered","items":["Parçalı fonksiyon f(x) = { x², x ≥ 2; 5x-2, x \u003c 2 } sorusu çözülüyor.","f(2) = 2² = 4, f(-1) = 5(-1)-2 = -7, f(4) = 4² = 16 olarak hesaplanıyor.","Sonuç olarak f(4) - f(-1) - f(2) = 16 - (-7) - 4 = 19 olarak bulunuyor."]},"beginTime":1235,"endTime":1274,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1235&ask_summarization=1"},{"index":10,"title":"Fonksiyon Değer Soruları Çözüm Yöntemi","list":{"type":"unordered","items":["Öğrencilerin zorlandığı fonksiyon değer sorularında (f(x) bir'in f(x) türünden eşiti nedir gibi) şıklardan yola çıkarak çözüm yapılır.","Çözüm yönteminde, x yerine belirli değerler (örneğin 2, 10) yazarak fonksiyonun değerini hesaplayıp, şıklarda f(x) gördüğümüz yere bu değerleri yerleştirerek doğru cevabı buluruz.","Bu yöntemle farklı değerler (2, 10, 3) deneyerek doğru şıkı tespit edebiliriz."]},"beginTime":1288,"endTime":1639,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1288&ask_summarization=1"},{"index":11,"title":"Fonksiyonun Tanımı","list":{"type":"unordered","items":["Fonksiyonun tanımı f: A → B şeklindedir; burada A tanım kümesi, B değer kümesidir.","Görüntü kümesi, değer kümesindeki sadece gidilen yerlerdir ve fonksiyonun değerlerini hesaplayarak bulunabilir.","Fonksiyon için iki önemli kural vardır: Tanım kümesindeki her elemanın değer kümesine gideceği ve bir elemanın aynı anda sadece bir yere gidebileceği."]},"beginTime":1639,"endTime":1880,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1639&ask_summarization=1"},{"index":12,"title":"Fonksiyon Tanımı ve Örnekler","list":{"type":"unordered","items":["Fonksiyon, sözünü eri olmalı ve ne diyorsa onu yapması gerekir.","Tam sayıları tam sayılara götürme ifadesi fonksiyon değildir çünkü 2'yi 6/5'e götürüyor ve 6/5 tam sayı değildir.","Tam sayıları reel sayılara götürme ifadesi 3'ü götüremiyor çünkü paydayı sıfır yapıyor, bu yüzden fonksiyon değildir."]},"beginTime":1883,"endTime":1956,"href":"/video/preview/3468484602478176835?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1883&ask_summarization=1"},{"index":13,"title":"Fonksiyon Olmayan ve Olan İfadeler","list":{"type":"unordered","items":["Tam sayıları (3 hariç) götürme ifadesi fonksiyondur çünkü 3 hariç diğer sayıları götürebilir.","Eğer payda x²-9 olsaydı, hem 3 hem de -3 paydayı sıfır yaptığı için fonksiyon olmazdı.","Reel sayıları reel sayılara götürme ifadesi fonksiyon değildir çünkü kök içinde eksi üç 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Öğretmen, tahtada notlar alarak konuyu adım adım açıklamaktadır.","Video, ters fonksiyonun tanımı ve çözüm yöntemlerini, doğrusal fonksiyonlarda ters fonksiyon bulma, tam kareli ve tam küp ifadelerde ters fonksiyon hesaplama, kesirli ifadelerde ters fonksiyon bulma ve birebir-örten fonksiyonların tersinin bulunması gibi konuları ele almaktadır. Ayrıca bileşke fonksiyonların nasıl çözüleceği, f(g(x)) ve g(f(x)) gibi bileşke fonksiyonların hesaplanması ve görüntü kümesinin belirlenmesi gibi konular da detaylı şekilde anlatılmaktadır.","Videoda 2023 AYT ve TYT sınavlarından alınan sorular çözülerek konular pekiştirilmekte, \"ilk aşkımın baş harfini yazma\" yöntemi gibi pratik çözümler sunulmakta ve \"Emrah filmleri\" örneği üzerinden bileşke fonksiyonların tanımı somutlaştırılmaktadır. Video, bir sonraki dersin grafik olacağını belirterek sona ermektedir."]},"endTime":3908,"title":"Matematik Dersi: Ters Fonksiyon ve Bileşke Fonksiyonlar","beginTime":0}],"fullResult":[{"index":0,"title":"Ters Fonksiyon Kavramı","list":{"type":"unordered","items":["Ters fonksiyon, f(x) = y denkleminde içerideki ile dışarıdakini yer değiştirdiğinizde üzerine eksi bir gelir.","Ters fonksiyon soruları ikiye ayrılır: sayılı sorular ve sayısız sorular.","Sayısız sorularda yer değiştirme yapılmaz, ancak sayılı sorularda yer değiştirme yapılır."]},"beginTime":0,"endTime":54,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=0&ask_summarization=1"},{"index":1,"title":"Sayısız Ters Fonksiyon Soruları","list":{"type":"unordered","items":["Sayısız sorularda yer değiştirme yaparak f(x) ve f⁻¹(x) ifadelerini birbirine eşitleriz.","f(x) ve f⁻¹(x) ifadeleri eşit olduğunda, içindekiler birbirine eşittir.","Çözümde önce içindekiler eşitlenir, sonra dışarıdakiler eşitlenir ve bilinmeyenler bulunur."]},"beginTime":54,"endTime":217,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=54&ask_summarization=1"},{"index":2,"title":"Sayısal Ters Fonksiyon Soruları","list":{"type":"unordered","items":["Sayısal sorularda f⁻¹(x) verilmişse, içindekileri istenen değere eşitleyerek çözüm yapılır.","f⁻¹(x) verilmişse, önce içindekileri istenen değere eşitleriz, sonra f(x) değerini buluruz.","Çözümde önce içindekiler eşitlenir, sonra dışarıdakiler eşitlenir ve bilinmeyenler bulunur."]},"beginTime":217,"endTime":324,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=217&ask_summarization=1"},{"index":3,"title":"Karmaşık Ters Fonksiyon Sorusu","list":{"type":"unordered","items":["Karmaşık ters fonksiyon sorularında, f⁻¹(x) = x² - 1 ve f(x) = x + f(x) gibi denklemler kullanılır.","Çözümde önce denklemler karşıya atılır, sonra eksi bir işareti yok edilir.","Çözümde önce içindekiler eşitlenir, sonra dışarıdakiler eşitlenir ve bilinmeyenler bulunur."]},"beginTime":324,"endTime":445,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=324&ask_summarization=1"},{"index":4,"title":"Doğrusal Fonksiyonların Tersi","list":{"type":"unordered","items":["Doğrusal fonksiyonlarda ters fonksiyon bulmak için basit bir kural geçerlidir: f(x) = ax + b fonksiyonunun tersi f⁻¹(x) = (x - b) / a şeklindedir.","Örneğin, f(x) = 5x - 4 fonksiyonunun tersi f⁻¹(x) = (x + 4) / 5, f(x) = 2x + 7 fonksiyonunun tersi f⁻¹(x) = (x - 7) / 2, f(x) = 10x - 1 fonksiyonunun tersi f⁻¹(x) = (x + 1) / 10'dur.","f(x) = -3x + 4 fonksiyonunun tersi f⁻¹(x) = (x + 3) / 4'tür."]},"beginTime":449,"endTime":528,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=449&ask_summarization=1"},{"index":5,"title":"Orijinal Çözüm Yöntemi","list":{"type":"unordered","items":["Doğrusal olmayan fonksiyonların tersini bulmak için orijinal çözüm yöntemi kullanılır: f(x) = m şeklinde yazılır ve x bulunur.","f⁻¹(x) = m şeklinde yazılan fonksiyonda x yerine x yazılır ve x bulunur.","Örneğin, f(x) = 4√(x+1) / 5 fonksiyonunun tersi f⁻¹(x) = (3x - 4) / 2'dir."]},"beginTime":528,"endTime":817,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=528&ask_summarization=1"},{"index":6,"title":"Tam Kareli ve Küplü İfadelerde Ters Fonksiyon","list":{"type":"unordered","items":["Tam kareli ifadelerde tersini bulmak için ifadeyi tam kareye çevirmek gerekir, bu için yan tarafı ikiye bölmek yeterlidir.","Küplü ifadelerde tersini bulmak için ifadeyi tam küpeye çevirmek gerekir, bu için yan tarafı üç'e bölmek yeterlidir.","Örneğin, f(x) = x² - 6x + 9 fonksiyonunun tersi f⁻¹(x) = -√(x - 9) + 3'tür.","f(x) = x³ - 48x + 124 fonksiyonunun tersi f⁻¹(x) = ³√(x - 124) + 4'tür."]},"beginTime":817,"endTime":1067,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=817&ask_summarization=1"},{"index":7,"title":"Fonksiyonların Tersi","list":{"type":"unordered","items":["Fonksiyonun tersini bulmak için pratik bir yöntem vardır: üstteki x'in katsayısı ile alttaki sabit terimin yerleri ve işaretleri değişir.","Fonksiyonun tanım kümesi ile tersinin tanım kümesi yer değiştirir.","Fonksiyonun tersini bulmak için paydayı sıfır yapan değerler çıkarılır."]},"beginTime":1071,"endTime":1170,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1071&ask_summarization=1"},{"index":8,"title":"Fonksiyonların Tersi Örnekleri","list":{"type":"unordered","items":["f(x) = (5x-1)/(2x+4) fonksiyonunun tersi f⁻¹(x) = (-4x-1)/(2x-5) olarak bulunur.","f⁻¹ fonksiyonunun tanım kümesinde paydayı sıfır yapan değerler çıkarılır.","Fonksiyonun tersini bulmak için üstteki x'in katsayısı ile alttaki sabit terimin yerleri ve işaretleri değişir."]},"beginTime":1170,"endTime":1299,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1170&ask_summarization=1"},{"index":9,"title":"Fonksiyonların Tersi Özellikleri","list":{"type":"unordered","items":["Bir fonksiyonun tersi için birebir ve örten olması gerekir, aksi takdirde tersi fonksiyon olmaz.","Fonksiyonun grafiği verildiğinde, tersinin grafiği y=x doğrusuna göre simetriği olarak bulunur.","Fonksiyonun tersini bulmak için yatay çizgi testi yapılır; yatay çizgi fonksiyonu iki noktada keserse birebir değildir."]},"beginTime":1299,"endTime":1434,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1299&ask_summarization=1"},{"index":10,"title":"Bileşke Fonksiyonlar","list":{"type":"unordered","items":["Bileşke fonksiyonlarda f∘g(x) ifadesi f(g(x)) anlamına gelir ve parantezle gösterilir.","Bileşke fonksiyonlarda önce içteki fonksiyonun değeri bulunur, sonra dıştaki fonksiyonun değeri hesaplanır.","Bileşke fonksiyonlarda pratik çözüm yöntemi: sağdaki fonksiyonun x gördüğünüz yere soldaki fonksiyonun değeri 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yolu, o fonksiyonun tersini yanına yapıştırmaktır.","Bileşke fonksiyonlarda, sağdaki fonksiyonu tutup soldaki x gördüğünüz yere yapıştırmanız gerekir."]},"beginTime":1780,"endTime":1909,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1780&ask_summarization=1"},{"index":13,"title":"Örnek Problemler","list":{"type":"unordered","items":["3x-2 fonksiyonunun tersi x+2'dir ve bu fonksiyonun tersi ile birleştirildiğinde g(x) elde edilir.","2x-4 bileşke g'nin tersi (x+2/3) şeklinde hesaplanır.","f(x) fonksiyonunu bulmak için, f(g(x)) ifadesinde g'nin tersini sağdan yapıştırarak f(x) elde edilir."]},"beginTime":1909,"endTime":2104,"href":"/video/preview/17251212286532646209?parent-reqid=1769669846212041-16645863625064675163-balancer-l7leveler-kubr-yp-sas-257-BAL&text=Mustafa+Guler&t=1909&ask_summarization=1"},{"index":14,"title":"Fonksiyonların Tersi ve 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