Find g(f(x)) f(x)=3x-12 , g(x)=x/3+4

$f (x) = 3 x - 12$ , $g (x) = \frac{x}{3} + 4$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 12)$ by substituting in the value of $f$ into $g$ .

$g (3 x - 12) = \frac{3 x - 12}{3} + 4$

Step 3

Cancel the common factor of $3 x - 12$ and $3$ .

Factor $3$ out of $3 x$ .

$g (3 x - 12) = \frac{3 (x) - 12}{3} + 4$

Factor $3$ out of $- 12$ .

$g (3 x - 12) = \frac{3 (x) + 3 \cdot - 4}{3} + 4$

Factor $3$ out of $3 (x) + 3 (- 4)$ .

$g (3 x - 12) = \frac{3 (x - 4)}{3} + 4$

Cancel the common factors.

Factor $3$ out of $3$ .

$g (3 x - 12) = \frac{3 (x - 4)}{3 (1)} + 4$

Cancel the common factor.

$g (3 x - 12) = \frac{3 (x - 4)}{3 \cdot 1} + 4$

Rewrite the expression.

$g (3 x - 12) = \frac{x - 4}{1} + 4$

Divide $x - 4$ by $1$ .

$g (3 x - 12) = x - 4 + 4$

Step 4

Combine the opposite terms in $x - 4 + 4$ .

Add $- 4$ and $4$ .

$g (3 x - 12) = x + 0$

Add $x$ and $0$ .

$g (3 x - 12) = x$