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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} - 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $3$ .

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

Multiply $3$ by $- 3$ .

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

Step 4

Subtract $3$ from $- 9$ .

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