Answer
$(f \circ g)(x) = f(g(x)) = 2x + 28$
Work Step by Step
In this problem, we are asked to evaluate a composite function. We will use the inner function and substitute it where we see $x$ in the outer function. This means that $(f \circ g)(x) = f(g(x))$, so where we see $x$ in the $f(x)$ function, we will plug in the function $g(x)$.
To evaluate $f(g(x))$, we begin by plugging in the function $g(x)$ where we see $x$ in the outer function, $f(x)$:
$f(g(x)) = 4(\frac{1}{2}x + 7)$
Use distributive property to multiply the coefficient with each term of the binomial in the composite function first:
$f(g(x)) = (4)(\frac{1}{2}x) + (4)(7)$
Multiply to simplify:
$f(g(x)) = \frac{4}{2}x + 28$
Divide numerator and denominator by their greatest common factor, which is $2$, in this case:
$f(g(x)) = 2x + 28$