Find f(g(x)) f(x)=3x-3 , g(x)=1/3x+4

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

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{1}{3} x + 4)$ by substituting in the value of $g$ into $f$ .

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

Simplify each term.

Combine $\frac{1}{3}$ and $x$ .

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $4$ .

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

Subtract $3$ from $12$ .

$f (\frac{1}{3} x + 4) = x + 9$