# 123456780124

**URL:** <https://sorumatik.co/t/topic/84708>\
**Category:** Makine Mühendisliği\
**Tags:** matematik\
**Created:** [Ağustos 7, 2024, 6:06ös UTC](https://sorumatik.co/t/topic/84708 "2024-08-07T18:06:25Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![buraktürk](https://sorumatik.co/letter_avatar_proxy/v4/letter/b/5e9695/32.png) [@buraktürk](https://sorumatik.co/u/burakt%C3%BCrk)\
**Post date:** [Ağustos 7, 2024, 6:06ös UTC](https://sorumatik.co/t/topic/84708/1 "2024-08-07T18:06:26Z")

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@sorumatikbot  
!Ekran görüntüsü 2024-08-07 210600|672x500 [Link Silindi]

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**Author:** ![Sorumatik\_Ogretmen](https://sorumatik.co/user_avatar/sorumatik.co/sorumatik_ogretmen/32/30517_2.png) [@Sorumatik\_Ogretmen](https://sorumatik.co/u/Sorumatik_Ogretmen)\
**Post date:** [Ağustos 7, 2024, 6:06ös UTC](https://sorumatik.co/t/topic/84708/2 "2024-08-07T18:06:37Z")

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## **Given f(x) = \frac{x-1}{x-2} and g(x) = x^2 . Solve for f(g(x)) = 5**

**Answer:**

To solve for f(g(x)) = 5 , we first need to find an expression for f(g(x)) :

1. **Calculate g(x) :**  
 g(x) = x^2 

2. **Substitute g(x) into f(x) :**

3. **Set up the equation f(g(x)) = 5 :**

4. **Solve for x :**  
Multiply both sides by x^2 - 2 :

5. **Check the solutions:**

**The solution set is:** \left\{ -\frac{3}{2}, \frac{3}{2} \right\} , which corresponds to option (I).

Therefore, the correct answer is **(I) \left\{ -\frac{3}{2}, \frac{3}{2} \right\}**.