Find f(g(x)) f(x)=4x+1 , g(x)=x^2-5

$f (x) = 4 x + 1$ , $g (x) = x^{2} - 5$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} - 5) = 4 (x^{2} - 5) + 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} - 5) = 4 x^{2} + 4 \cdot - 5 + 1$

Multiply $4$ by $- 5$ .

$f (x^{2} - 5) = 4 x^{2} - 20 + 1$

Step 4

Add $- 20$ and $1$ .

$f (x^{2} - 5) = 4 x^{2} - 19$