Answer
$g(f(x)) = 2x + 7$
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 $g(f(x))$, we begin by plugging in the function $f(x)$ where we see $x$ in the outer function, $g(x)$:
$g(f(x)) = \frac{1}{2}(4x) + 7$
Multiply first, according to order of operations:
$g(f(x)) = \dfrac{4x}{2} + 7$
Reduce the fraction by multiplying both numerator and denominator by their greatest common factor: $2$.
$g(f(x)) = 2x + 7$
