https://file.aiquickdraw.com/mathbot/file/17265774070039puj5eli.jpg

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!

Find the function g(x), given that: (f ∘ g)(x) = 2x + 5 and f(x) = x + 6.

Learn how to solve a function composition problem where (f ∘ g)(x) = 2x + 5 and f(x) = x + 6. This solution explains how to find the function g(x) step by step, covering key algebraic concepts and function composition principles. Suitable for students in Grades 9-11.

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