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

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

Set up the composite result function.

$f (g (x))$

Evaluate $f (2 x + 2)$ by substituting in the value of $g$ into $f$ .

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

Simplify each term.

Rewrite ${(2 x + 2)}^{2}$ as $(2 x + 2) (2 x + 2)$ .

$f (2 x + 2) = (2 x + 2) (2 x + 2) - 3 (2 x + 2)$

Expand $(2 x + 2) (2 x + 2)$ using the FOIL Method.

Apply the distributive property.

$f (2 x + 2) = 2 x (2 x + 2) + 2 (2 x + 2) - 3 (2 x + 2)$

Apply the distributive property.

$f (2 x + 2) = 2 x (2 x) + 2 x \cdot 2 + 2 (2 x + 2) - 3 (2 x + 2)$

Apply the distributive property.

$f (2 x + 2) = 2 x (2 x) + 2 x \cdot 2 + 2 (2 x) + 2 \cdot 2 - 3 (2 x + 2)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (2 x + 2) = 2 \cdot (2 x \cdot x) + 2 x \cdot 2 + 2 (2 x) + 2 \cdot 2 - 3 (2 x + 2)$

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

Move $x$ .

$f (2 x + 2) = 2 \cdot (2 (x \cdot x)) + 2 x \cdot 2 + 2 (2 x) + 2 \cdot 2 - 3 (2 x + 2)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $2$ .

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

Add $4 x$ and $4 x$ .

$f (2 x + 2) = 4 x^{2} + 8 x + 4 - 3 (2 x + 2)$

Apply the distributive property.

$f (2 x + 2) = 4 x^{2} + 8 x + 4 - 3 (2 x) - 3 \cdot 2$

Multiply $2$ by $- 3$ .

$f (2 x + 2) = 4 x^{2} + 8 x + 4 - 6 x - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$f (2 x + 2) = 4 x^{2} + 8 x + 4 - 6 x - 6$

Simplify by adding terms.

Subtract $6 x$ from $8 x$ .

$f (2 x + 2) = 4 x^{2} + 2 x + 4 - 6$

Subtract $6$ from $4$ .

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