Find f(g(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.

$f (g (x))$

Step 2

Evaluate $f (\frac{x}{3} + 5)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $5$ .

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

Step 4

Combine the opposite terms in $x + 15 - 15$ .

Subtract $15$ from $15$ .

$f (\frac{x}{3} + 5) = x + 0$

Add $x$ and $0$ .

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