Find f(g(x)) f(x)=x^2-8 , g(x)=4x-4

$f (x) = x^{2} - 8$ , $g (x) = 4 x - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (4 x - 4) = {(4 x - 4)}^{2} - 8$

Step 3

Simplify each term.

Rewrite ${(4 x - 4)}^{2}$ as $(4 x - 4) (4 x - 4)$ .

$f (4 x - 4) = (4 x - 4) (4 x - 4) - 8$

Expand $(4 x - 4) (4 x - 4)$ using the FOIL Method.

Apply the distributive property.

$f (4 x - 4) = 4 x (4 x - 4) - 4 (4 x - 4) - 8$

Apply the distributive property.

$f (4 x - 4) = 4 x (4 x) + 4 x \cdot - 4 - 4 (4 x - 4) - 8$

Apply the distributive property.

$f (4 x - 4) = 4 x (4 x) + 4 x \cdot - 4 - 4 (4 x) - 4 \cdot - 4 - 8$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (4 x - 4) = 4 \cdot (4 x \cdot x) + 4 x \cdot - 4 - 4 (4 x) - 4 \cdot - 4 - 8$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$f (4 x - 4) = 4 \cdot (4 (x \cdot x)) + 4 x \cdot - 4 - 4 (4 x) - 4 \cdot - 4 - 8$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$f (4 x - 4) = 16 x^{2} + 4 x \cdot - 4 - 4 (4 x) - 4 \cdot - 4 - 8$

Multiply $- 4$ by $4$ .

$f (4 x - 4) = 16 x^{2} - 16 x - 4 (4 x) - 4 \cdot - 4 - 8$

Multiply $4$ by $- 4$ .

$f (4 x - 4) = 16 x^{2} - 16 x - 16 x - 4 \cdot - 4 - 8$

Multiply $- 4$ by $- 4$ .

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

Subtract $16 x$ from $- 16 x$ .

$f (4 x - 4) = 16 x^{2} - 32 x + 16 - 8$

Step 4

Subtract $8$ from $16$ .

$f (4 x - 4) = 16 x^{2} - 32 x + 8$