Find g(f(x)) f(x)=2x-6 , g(x)=(x+2)/6

$f (x) = 2 x - 6$ , $g (x) = \frac{x + 2}{6}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (2 x - 6)$ by substituting in the value of $f$ into $g$ .

$g (2 x - 6) = \frac{(2 x - 6) + 2}{6}$

Step 3

Cancel the common factor of $(2 x - 6) + 2$ and $6$ .

Factor $2$ out of $2 x$ .

$g (2 x - 6) = \frac{2 (x) - 6 + 2}{6}$

Factor $2$ out of $- 6$ .

$g (2 x - 6) = \frac{2 (x) + 2 \cdot - 3 + 2}{6}$

Factor $2$ out of $2 (x) + 2 (- 3)$ .

$g (2 x - 6) = \frac{2 (x - 3) + 2}{6}$

Factor $2$ out of $2$ .

$g (2 x - 6) = \frac{2 (x - 3) + 2 (1)}{6}$

Factor $2$ out of $2 (x - 3) + 2 (1)$ .

$g (2 x - 6) = \frac{2 (x - 3 + 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$g (2 x - 6) = \frac{2 (x - 3 + 1)}{2 (3)}$

Cancel the common factor.

$g (2 x - 6) = \frac{2 (x - 3 + 1)}{2 \cdot 3}$

Rewrite the expression.

$g (2 x - 6) = \frac{x - 3 + 1}{3}$

Step 4

Add $- 3$ and $1$ .

$g (2 x - 6) = \frac{x - 2}{3}$