Find g(f(x)) f(x)=x^2-25 , g(x)=2x+3

$f (x) = x^{2} - 25$ , $g (x) = 2 x + 3$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 25)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 25) = 2 (x^{2} - 25) + 3$

Step 3

Simplify each term.

Apply the distributive property.

$g (x^{2} - 25) = 2 x^{2} + 2 \cdot - 25 + 3$

Multiply $2$ by $- 25$ .

$g (x^{2} - 25) = 2 x^{2} - 50 + 3$

Step 4

Add $- 50$ and $3$ .

$g (x^{2} - 25) = 2 x^{2} - 47$