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.