Find g(f(x)) f(x)=2x^2+x-4 g(x)=-4x-15

$f (x) = 2 x^{2} + x - 4$ $g (x) = - 4 x - 15$

Set up the composite result function.

$g (f (x))$

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

$g (2 x^{2} + x - 4) = - 4 (2 x^{2} + x - 4) - 15$

Simplify each term.

Apply the distributive property.

$g (2 x^{2} + x - 4) = - 4 (2 x^{2}) - 4 x - 4 \cdot - 4 - 15$

Simplify.

Multiply $2$ by $- 4$ .

$g (2 x^{2} + x - 4) = - 8 x^{2} - 4 x - 4 \cdot - 4 - 15$

Multiply $- 4$ by $- 4$ .

$g (2 x^{2} + x - 4) = - 8 x^{2} - 4 x + 16 - 15$

Subtract $15$ from $16$ .

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