Find f(g(x)) f(x)=18-3x , g(x)=6-x/3

$f (x) = 18 - 3 x$ , $g (x) = 6 - \frac{x}{3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (6 - \frac{x}{3})$ by substituting in the value of $g$ into $f$ .

$f (6 - \frac{x}{3}) = 18 - 3 (6 - \frac{x}{3})$

Step 3

Simplify each term.

Apply the distributive property.

$f (6 - \frac{x}{3}) = 18 - 3 \cdot 6 - 3 (- \frac{x}{3})$

Multiply $- 3$ by $6$ .

$f (6 - \frac{x}{3}) = 18 - 18 - 3 (- \frac{x}{3})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$f (6 - \frac{x}{3}) = 18 - 18 - 3 \frac{- x}{3}$

Factor $3$ out of $- 3$ .

$f (6 - \frac{x}{3}) = 18 - 18 + 3 (- 1) (\frac{- x}{3})$

Cancel the common factor.

$f (6 - \frac{x}{3}) = 18 - 18 + 3 \cdot (- 1 \frac{- x}{3})$

Rewrite the expression.

$f (6 - \frac{x}{3}) = 18 - 18 - 1 (- x)$

Multiply $- 1$ by $- 1$ .

$f (6 - \frac{x}{3}) = 18 - 18 + 1 x$

Multiply $x$ by $1$ .

$f (6 - \frac{x}{3}) = 18 - 18 + x$

Step 4

Simplify by subtracting numbers.

Subtract $18$ from $18$ .

$f (6 - \frac{x}{3}) = 0 + x$

Add $0$ and $x$ .

$f (6 - \frac{x}{3}) = x$