Find f(g(x)) f(x)=5x-2 g(x)=4x^2-4

$f (x) = 5 x - 2$ $g (x) = 4 x^{2} - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (4 x^{2} - 4) = 5 (4 x^{2} - 4) - 2$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x^{2} - 4) = 5 (4 x^{2}) + 5 \cdot - 4 - 2$

Multiply $4$ by $5$ .

$f (4 x^{2} - 4) = 20 x^{2} + 5 \cdot - 4 - 2$

Multiply $5$ by $- 4$ .

$f (4 x^{2} - 4) = 20 x^{2} - 20 - 2$

Step 4

Subtract $2$ from $- 20$ .

$f (4 x^{2} - 4) = 20 x^{2} - 22$