Answer
$f(g(x)) = 12x^2 + 2$
$g(f(x)) = 6x^2 + 4$
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, $f(x)$:
$f(g(x)) = 3(2x)^2 + 2$
Evaluate exponents first, according to order of operations:
$f(g(x)) = 3(4x^2) + 2$
Multiply to simplify:
$f(g(x)) = 12x^2 + 2$
To evaluate $g(f(x))$, we begin by plugging in the function $f(x)$ where we see $x$ in the outer function, $g(x)$:
$g(f(x)) = 2(3x^2 + 2)$
Use distributive property to multiply coefficient with all terms within the parentheses:
$g(f(x)) = 6x^2 + 4$
