Find f(g(x)) f(x) = square root of x+9 ; g(x)=8x-13

$f (x) = \sqrt{x + 9}$ ; $g (x) = 8 x - 13$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (8 x - 13)$ by substituting in the value of $g$ into $f$ .

$f (8 x - 13) = \sqrt{(8 x - 13) + 9}$

Step 3

Add $- 13$ and $9$ .

$f (8 x - 13) = \sqrt{8 x - 4}$

Step 4

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

Factor $4$ out of $8 x$ .

$f (8 x - 13) = \sqrt{4 (2 x) - 4}$

Factor $4$ out of $- 4$ .

$f (8 x - 13) = \sqrt{4 (2 x) + 4 (- 1)}$

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

$f (8 x - 13) = \sqrt{4 (2 x - 1)}$

Step 5

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

$f (8 x - 13) = \sqrt{2^{2} (2 x - 1)}$

Step 6

Pull terms out from under the radical.

$f (8 x - 13) = 2 \sqrt{2 x - 1}$