Find f(g(x)) f(x)=x^2-1 , g(x)=2x-3

$f (x) = x^{2} - 1$ , $g (x) = 2 x - 3$

Set up the composite result function.

$f (g (x))$

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

$f (2 x - 3) = {(2 x - 3)}^{2} - 1$

Simplify each term.

Rewrite ${(2 x - 3)}^{2}$ as $(2 x - 3) (2 x - 3)$ .

$f (2 x - 3) = (2 x - 3) (2 x - 3) - 1$

Expand $(2 x - 3) (2 x - 3)$ using the FOIL Method.

Apply the distributive property.

$f (2 x - 3) = 2 x (2 x - 3) - 3 (2 x - 3) - 1$

Apply the distributive property.

$f (2 x - 3) = 2 x (2 x) + 2 x \cdot - 3 - 3 (2 x - 3) - 1$

Apply the distributive property.

$f (2 x - 3) = 2 x (2 x) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3 - 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (2 x - 3) = 2 \cdot (2 x \cdot x) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3 - 1$

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

Move $x$ .

$f (2 x - 3) = 2 \cdot (2 (x \cdot x)) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3 - 1$

Multiply $x$ by $x$ .

$f (2 x - 3) = 2 \cdot (2 x^{2}) + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3 - 1$

Multiply $2$ by $2$ .

$f (2 x - 3) = 4 x^{2} + 2 x \cdot - 3 - 3 (2 x) - 3 \cdot - 3 - 1$

Multiply $- 3$ by $2$ .

$f (2 x - 3) = 4 x^{2} - 6 x - 3 (2 x) - 3 \cdot - 3 - 1$

Multiply $2$ by $- 3$ .

$f (2 x - 3) = 4 x^{2} - 6 x - 6 x - 3 \cdot - 3 - 1$

Multiply $- 3$ by $- 3$ .

$f (2 x - 3) = 4 x^{2} - 6 x - 6 x + 9 - 1$

Subtract $6 x$ from $- 6 x$ .

$f (2 x - 3) = 4 x^{2} - 12 x + 9 - 1$

Subtract $1$ from $9$ .

$f (2 x - 3) = 4 x^{2} - 12 x + 8$