Find g(f(x)) f(x)=3x-2 , g(x)=(x+2)/3

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 2)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify the numerator.

Add $- 2$ and $2$ .

$g (3 x - 2) = \frac{3 x + 0}{3}$

Add $3 x$ and $0$ .

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$g (3 x - 2) = x$