Find g(f(x)) f(x)=x^2+4x-1 g(x)=2x-7

$f (x) = x^{2} + 4 x - 1$ $g (x) = 2 x - 7$

Set up the composite result function.

$g (f (x))$

Evaluate $g (x^{2} + 4 x - 1)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} + 4 x - 1) = 2 (x^{2} + 4 x - 1) - 7$

Simplify each term.

Apply the distributive property.

$g (x^{2} + 4 x - 1) = 2 x^{2} + 2 (4 x) + 2 \cdot - 1 - 7$

Simplify.

Multiply $4$ by $2$ .

$g (x^{2} + 4 x - 1) = 2 x^{2} + 8 x + 2 \cdot - 1 - 7$

Multiply $2$ by $- 1$ .

$g (x^{2} + 4 x - 1) = 2 x^{2} + 8 x - 2 - 7$

Subtract $7$ from $- 2$ .

$g (x^{2} + 4 x - 1) = 2 x^{2} + 8 x - 9$