Find f(g(x)) f(x)=-2x^2+2x+3 g(x)=-4

$f (x) = - 2 x^{2} + 2 x + 3$ $g (x) = - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 4)$ by substituting in the value of $g$ into $f$ .

$f (- 4) = - 2 {(- 4)}^{2} + 2 (- 4) + 3$

Step 3

Simplify each term.

Raise $- 4$ to the power of $2$ .

$f (- 4) = - 2 \cdot 16 + 2 (- 4) + 3$

Multiply $- 2$ by $16$ .

$f (- 4) = - 32 + 2 (- 4) + 3$

Multiply $2$ by $- 4$ .

$f (- 4) = - 32 - 8 + 3$

Step 4

Simplify by adding and subtracting.

Subtract $8$ from $- 32$ .

$f (- 4) = - 40 + 3$

Add $- 40$ and $3$ .

$f (- 4) = - 37$