Answer
$h(g(x)) = -x - 10$
Work Step by Step
In this problem, we are asked to evaluate composite functions. We will use the inner function and substitute it where we see $x$ in the outer function.
To evaluate $h(g(x))$, we begin by plugging in the function $g(x)$ where we see $x$ in the outer function, $h(x)$:
$h(g(x)) = -2[\frac{1}{2}(x)] + 7) + 4$
Multiply first, according to order of operations:
$h(g(x)) = (-\frac{2x}{2} - 14) + 4$
Reduce the fraction by multiplying both numerator and denominator by their greatest common factor: $2$.
$h(g(x)) = -x - 14 + 4$
Combine like terms:
$h(g(x)) = -x - 10$
