Answer
$f(g(x)) = x - 2$
$g(f(x)) = x - 2$
Work Step by Step
For these types of problems, 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 $f(g(x))$, we begin by plugging in the function $g(x)$ where we see $x$ in the outer function, $f(x)$:
$f(g(x)) = (x - 5) + 3$
Combine like terms:
$f(g(x)) = x - 2$
To evaluate $g(f(x))$, we begin by plugging in the function $f(x)$ where we see $x$ in the outer function, $g(x)$:
$g(f(x)) = (x + 3) - 5$
Combine like terms:
$g(f(x)) = x - 2$
