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The image you provided contains a mathematical problem in Indonesian. It can be translated as:

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**7. Diketahui** \( f(x) = x + 3 \) **dan** \( (g \circ f)(x) = x^2 + 2x - 5 \). **Tentukan fungsi** \( g(x) \)!

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This problem asks to find the function \( g(x) \), given that \( f(x) = x + 3 \) and the composition \( (g \circ f)(x) = x^2 + 2x - 5 \).

### Solution Outline:

We are given:

1. \( f(x) = x + 3 \)
2. \( (g \circ f)(x) = g(f(x)) = x^2 + 2x - 5 \)

Now, \( (g \circ f)(x) \) means that we first apply the function \( f(x) \) and then apply \( g(x) \) to the result of \( f(x) \). So, to find \( g(x) \), we need to express \( g \) as a function of \( f(x) \).

#### Steps:
- \( f(x) = x + 3 \)
- So, \( g(f(x)) = g(x + 3) = x^2 + 2x - 5 \)

Let’s solve this equation for \( g(u) \) where \( u = f(x) = x + 3 \).

This gives:

\[
g(u) = (u - 3)^2 + 2(u - 3) - 5
\]

Simplifying this expression will give the function \( g(u) \).

Let me know if you'd like a step-by-step breakdown of the simplification process!

Would you like the details or have any questions? Here are some related questions that could help further your understanding:

1. What is function composition, and how is it applied in this problem?
2. How do you find the inverse of a function, and when is it necessary?
3. How would this problem change if \( f(x) \) were a different function?
4. How do transformations of functions like shifting and scaling work?
5. What are some common applications of function composition in real-world scenarios?

**Tip**: When dealing with function compositions, it’s helpful to rewrite the composition explicitly step by step to avoid confusion.

Diketahui f(x) = x + 3 dan (g ∘ f)(x) = x^2 + 2x - 5. Tentukan fungsi g(x)!

Learn how to determine the function g(x) given that f(x) = x + 3 and (g ∘ f)(x) = x^2 + 2x - 5. This problem involves concepts of function composition and quadratic functions, suitable for students in Grades 10-12.

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