Answer
$a^2 + 6a + 9$
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 $f(g(-a))$:
Let's begin by plugging in our value of $-a$ into the inner function $g(x)$:
$g(-a) = (-a) - 3$
Get rid of the parentheses because they are no longer needed:
$g(-a) = -a - 3$
Now, we will use the output $-a - 3$ to plug in for $x$ in the outer function $f(x)$:
$f(g(-a)) = (-a - 3)^2$
Rewrite as a product of binomials:
$f(g(-a)) = (-a - 3)(-a - 3)$
Use the FOIL method to expand the binomial. We will multiply the first terms, the outer terms, the inner terms, and the last terms:
$f(g(-a)) = (-a)(-a) - (3)(-a) - (3)(-a) + (-3)(-3)$
Multiply to simplify:
$f(g(-a)) = a^2 + 3a + 3a + 9$
Combine like terms:
$f(g(-a)) = a^2 + 6a + 9$
