Find f(g(x)) f(x) = square root of x+8 , g(x)=8x-12

$f (x) = \sqrt{x + 8}$ , $g (x) = 8 x - 12$

Set up the composite result function.

$f (g (x))$

Evaluate $f (8 x - 12)$ by substituting in the value of $g$ into $f$ .

$f (8 x - 12) = \sqrt{(8 x - 12) + 8}$

Add $- 12$ and $8$ .

$f (8 x - 12) = \sqrt{8 x - 4}$

Factor $4$ out of $8 x - 4$ .

Factor $4$ out of $8 x$ .

$f (8 x - 12) = \sqrt{4 (2 x) - 4}$

Factor $4$ out of $- 4$ .

$f (8 x - 12) = \sqrt{4 (2 x) + 4 (- 1)}$

Factor $4$ out of $4 (2 x) + 4 (- 1)$ .

$f (8 x - 12) = \sqrt{4 (2 x - 1)}$

Rewrite $4$ as $2^{2}$ .

$f (8 x - 12) = \sqrt{2^{2} (2 x - 1)}$

Pull terms out from under the radical.

$f (8 x - 12) = 2 \sqrt{2 x - 1}$