Find f(g(x)) f(x)=4x-1 , g(x)=x^2+7

$f (x) = 4 x - 1$ , $g (x) = x^{2} + 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (x^{2} + 7) = 4 (x^{2} + 7) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (x^{2} + 7) = 4 x^{2} + 4 \cdot 7 - 1$

Multiply $4$ by $7$ .

$f (x^{2} + 7) = 4 x^{2} + 28 - 1$

Step 4

Subtract $1$ from $28$ .

$f (x^{2} + 7) = 4 x^{2} + 27$