The problem in the image is written in Indonesian and asks to find the function $g(x)$ under certain conditions. Specifically, it says:

1. Find the function $g(x)$, given that: $(f \circ g)(x) = 2x + 5 \quad \text{and} \quad f(x) = x + 6$ where $(f \circ g)(x)$ means the composition of the functions $f$ and $g$, i.e., $f(g(x))$.

Solution:

We know that: $(f \circ g)(x) = f(g(x)) = 2x + 5$ Given that $f(x) = x + 6$, we can substitute this into the equation: $f(g(x)) = g(x) + 6$ Thus, we now have the equation: $g(x) + 6 = 2x + 5$ Solving for $g(x)$: $g(x) = 2x + 5 - 6$ $g(x) = 2x - 1$

So, the function $g(x)$ is: $g(x) = 2x - 1$

Would you like further details or explanations? Here are some related questions to expand your understanding:

1. How would you find $f(x)$ if $g(x)$ were given first?
2. What is the result of $(f \circ g)(x)$ for a general $f(x)$ and $g(x)$?
3. How does function composition work with different types of functions, such as quadratic or trigonometric functions?
4. Can the function $g(x)$ have multiple solutions in different contexts?
5. What is the domain of $g(x)$ and how does it relate to $f(x)$?

Tip: When working with function compositions, it's essential to substitute functions carefully and handle algebraic manipulations step by step!