Answer
$-\frac{8}{9}$
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 $f(f(0))$:
Let's begin by plugging in our value of $0$ into the inner function $f(x)$:
$f(0) = \frac{(0) - 2}{3}$
Subtract in the numerator:
$f(0) = -\frac{2}{3}$
Now, we will use the output $-\frac{2}{3}$ to plug in for $x$ in the outer function $f(x)$:
$f(f(0)) = \frac{(-\frac{2}{3}) - 2}{3}$
Find equivalent fractions in the numerator such that both denominators are the same, which is $3$, in this case:
$f(f(0)) = \frac{(-\frac{2}{3}) - \frac{6}{3}}{3}$
Subtract fractions in the numerator:
$f(f(0)) = \frac{-\frac{8}{3}}{3}$
Dividing by a number means multiplying by its reciprocal:
$f(f(0)) = (-\frac{8}{3})(\frac{1}{3})$
Multiply fractions to simplify:
$f(f(0)) = -\frac{8}{9}$
