To find \( g(f(x)) \), we need to substitute \( f(x) \) into \( g(x) \).

Given:
\[
f(x) = 3x + 2
\]
\[
g(x) = -x
\]

First, calculate \( f(x) \):
\[
f(x) = 3x + 2
\]

Now, substitute \( f(x) \) into \( g(x) \):
\[
g(f(x)) = g(3x + 2)
\]
Since \( g(x) = -x \), substitute \( x \) with \( 3x + 2 \):
\[
g(3x + 2) = -(3x + 2)
\]
Simplify:
\[
g(f(x)) = -3x - 2
\]

So, \( g(f(x)) = -3x - 2 \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the result of \( f(g(x)) \) given the same functions?
2. How do you find the inverse of \( f(x) \)?
3. What does the composition of two functions represent in terms of their graphs?
4. Can you find \( g(f(-1)) \)?
5. How do you determine if two functions are inverses of each other?

**Tip:** When working with function compositions, remember to carefully substitute the entire expression for the inner function into the outer function.

Explore how to compute g(f(x)) using function composition with detailed steps and examples. Learn about substitution in functions and its application in mathematical problems. Suitable for Grades 10-12.

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