Find g(f(x)) f(x)=x^2-7 , g(x)=3x-3

$f (x) = x^{2} - 7$ , $g (x) = 3 x - 3$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 7)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 7) = 3 (x^{2} - 7) - 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (x^{2} - 7) = 3 x^{2} + 3 \cdot - 7 - 3$

Multiply $3$ by $- 7$ .

$g (x^{2} - 7) = 3 x^{2} - 21 - 3$

Step 4

Subtract $3$ from $- 21$ .

$g (x^{2} - 7) = 3 x^{2} - 24$