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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x^{2} - 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $- 3$ .

$f (x^{2} - 3) = 4 x^{2} - 12 - 4$

Step 4

Subtract $4$ from $- 12$ .

$f (x^{2} - 3) = 4 x^{2} - 16$