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

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

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.