Find g(f(x)) f(x)=x^2-5 , g(x)=2x-3

$f (x) = x^{2} - 5$ , $g (x) = 2 x - 3$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 5)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 5) = 2 (x^{2} - 5) - 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (x^{2} - 5) = 2 x^{2} + 2 \cdot - 5 - 3$

Multiply $2$ by $- 5$ .

$g (x^{2} - 5) = 2 x^{2} - 10 - 3$

Step 4

Subtract $3$ from $- 10$ .

$g (x^{2} - 5) = 2 x^{2} - 13$