Answer
$a^4 + 8a^2 + 20$
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 rewrite this composite function as $h(h(a))$.
Let's begin by plugging in our value of $a$ into the inner function $h(x)$:
$h(a) = (a)^2 + 4$
Now we can get rid of the parentheses because they are not needed:
$h(a) = a^2 + 4$
Now, we will use the output $a^2 + 4$ to plug in for $x$ in the outer function $h(x)$:
$h(h(a)) = (a^2 + 4)^2 + 4$
Let's expand the binomial in parentheses:
$h(h(a)) = (a^2 + 4)(a^2 + 4) + 4$
Let's use the FOIL method to expand the binomial. We multiply the terms in this order: first terms, outer terms, inner terms, and, finally, last terms:
$h(h(a)) = ((a^2)(a^2) + (4)(a^2) + (4)(a^2) + (4)(4)) + 4$
Multiply to simplify:
$h(h(a)) = (a^4 + 4a^2 + 4a^2 + 16) + 4$
Add like terms:
$h(h(a)) = (a^4 + 8a^2 + 16) + 4$
Get rid of the parentheses and add the constants:
$h(h(a)) = a^4 + 8a^2 + 20$
