Find g(f(x)) f(x)=x^2-4 ; g(x)=2x+1

$f (x) = x^{2} - 4$ ; $g (x) = 2 x + 1$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (x^{2} - 4) = 2 (x^{2} - 4) + 1$

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

$g (x^{2} - 4) = 2 x^{2} - 8 + 1$

Step 4

Add $- 8$ and $1$ .

$g (x^{2} - 4) = 2 x^{2} - 7$