Find g(f(x)) f(x)=2x , g(x)=x^2+2x-1

$f (x) = 2 x$ , $g (x) = x^{2} + 2 x - 1$

Set up the composite result function.

$g (f (x))$

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

$g (2 x) = {(2 x)}^{2} + 2 (2 x) - 1$

Simplify each term.

Apply the product rule to $2 x$ .

$g (2 x) = 2^{2} x^{2} + 2 (2 x) - 1$

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

$g (2 x) = 4 x^{2} + 2 (2 x) - 1$

Multiply $2$ by $2$ .

$g (2 x) = 4 x^{2} + 4 x - 1$