Find g(f(x)) f(x)=3x-15 g(x)=x/3+5

$f (x) = 3 x - 15$ $g (x) = \frac{x}{3} + 5$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 15)$ by substituting in the value of $f$ into $g$ .

$g (3 x - 15) = \frac{3 x - 15}{3} + 5$

Step 3

Cancel the common factor of $3 x - 15$ and $3$ .

Factor $3$ out of $3 x$ .

$g (3 x - 15) = \frac{3 (x) - 15}{3} + 5$

Factor $3$ out of $- 15$ .

$g (3 x - 15) = \frac{3 (x) + 3 \cdot - 5}{3} + 5$

Factor $3$ out of $3 (x) + 3 (- 5)$ .

$g (3 x - 15) = \frac{3 (x - 5)}{3} + 5$

Cancel the common factors.

Factor $3$ out of $3$ .

$g (3 x - 15) = \frac{3 (x - 5)}{3 (1)} + 5$

Cancel the common factor.

$g (3 x - 15) = \frac{3 (x - 5)}{3 \cdot 1} + 5$

Rewrite the expression.

$g (3 x - 15) = \frac{x - 5}{1} + 5$

Divide $x - 5$ by $1$ .

$g (3 x - 15) = x - 5 + 5$

Step 4

Combine the opposite terms in $x - 5 + 5$ .

Add $- 5$ and $5$ .

$g (3 x - 15) = x + 0$

Add $x$ and $0$ .

$g (3 x - 15) = x$