Find h(g(x)) g(x)=2x and h(x)=x^2+4

$g (x) = 2 x$ and $h (x) = x^{2} + 4$

Set up the composite result function.

$h (g (x))$

Evaluate $h (2 x)$ by substituting in the value of $g$ into $h$ .

$h (2 x) = {(2 x)}^{2} + 4$

Simplify each term.

Apply the product rule to $2 x$ .

$h (2 x) = 2^{2} x^{2} + 4$

Raise $2$ to the power of $2$ .

$h (2 x) = 4 x^{2} + 4$