Answer
$-2$
Work Step by Step
For these types of problems where we are given a value to plug into composite functions, we evaluate the inner function first using the given value. Then we use the output of the inner function and substitute it where we see $x$ in the outer function. We can write this composite function as $f(g(-2))$:
Let's begin by plugging in our value of $-2$ into the inner function $g(x)$:
$g(-2) = 3(-2) + 2$
Multiply first:
$g(-2) = -6 + 2$
Add to simplify:
$g(-2) = -4$
Now, we will use the output $-4$ to plug in for $x$ in the outer function $f(x)$:
$f(g(-2)) = \frac{(-4) - 2}{3}$
Subtract to simplify:
$f(g(-2)) = \frac{-6}{3}$
Simplify the fraction:
$f(g(-2)) = -2$
