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The problem is asking to find \( f(g(x)) \), which is the composition of the functions \( f(x) \) and \( g(x) \).

Given:
\[
f(x) = 3x + 9
\]
\[
g(x) = 6x + 7
\]

To find \( f(g(x)) \), we substitute the expression for \( g(x) \) into \( f(x) \).

1. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(6x + 7)
\]
2. Now apply the function \( f \) to \( 6x + 7 \). Since \( f(x) = 3x + 9 \), replace \( x \) with \( 6x + 7 \):
\[
f(g(x)) = 3(6x + 7) + 9
\]
3. Expand and simplify the expression:
\[
f(g(x)) = 3 \cdot 6x + 3 \cdot 7 + 9 = 18x + 21 + 9 = 18x + 30
\]

So, the answer is:
\[
f(g(x)) = 18x + 30
\]

Let me know if you need any more details or clarification!

Here are some related questions you might find useful:
1. What is the composition \( g(f(x)) \)?
2. How do you find the domain of the composed function \( f(g(x)) \)?
3. What happens when you compose two quadratic functions instead of linear ones?
4. How does composition of functions differ from multiplication of functions?
5. What is the graphical interpretation of composing functions?

**Tip**: When composing functions, always substitute the second function into the first carefully, keeping track of the variables!

The functions f(x) = 3x + 9 and g(x) = 6x + 7 are given. Find f(g(x)) and provide your answer in its simplest form.

This problem explains how to find the composition of two linear functions f(x) = 3x + 9 and g(x) = 6x + 7. Step-by-step guidance is provided to calculate f(g(x)) and simplify the result.

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