Find g(f(x)) f(x)=8x-4 , g(x)=(x+8)/4

$f (x) = 8 x - 4$ , $g (x) = \frac{x + 8}{4}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (8 x - 4)$ by substituting in the value of $f$ into $g$ .

$g (8 x - 4) = \frac{(8 x - 4) + 8}{4}$

Step 3

Cancel the common factor of $(8 x - 4) + 8$ and $4$ .

Factor $4$ out of $8 x$ .

$g (8 x - 4) = \frac{4 (2 x) - 4 + 8}{4}$

Factor $4$ out of $- 4$ .

$g (8 x - 4) = \frac{4 (2 x) + 4 \cdot - 1 + 8}{4}$

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

$g (8 x - 4) = \frac{4 (2 x - 1) + 8}{4}$

Factor $4$ out of $8$ .

$g (8 x - 4) = \frac{4 (2 x - 1) + 4 \cdot 2}{4}$

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

$g (8 x - 4) = \frac{4 (2 x - 1 + 2)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$g (8 x - 4) = \frac{4 (2 x - 1 + 2)}{4 (1)}$

Cancel the common factor.

$g (8 x - 4) = \frac{4 (2 x - 1 + 2)}{4 \cdot 1}$

Rewrite the expression.

$g (8 x - 4) = \frac{2 x - 1 + 2}{1}$

Divide $2 x - 1 + 2$ by $1$ .

$g (8 x - 4) = 2 x - 1 + 2$

Step 4

Add $- 1$ and $2$ .

$g (8 x - 4) = 2 x + 1$