Find f(g(x)) f(x)=3/2x-6 , g(x)=(2x-12)/3

$f (x) = \frac{3}{2} x - 6$ , $g (x) = \frac{2 x - 12}{3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{2 x - 12}{3})$ by substituting in the value of $g$ into $f$ .

$f (\frac{2 x - 12}{3}) = \frac{3}{2} \cdot (\frac{2 x - 12}{3}) - 6$

Step 3

Simplify each term.

Factor $2$ out of $2 x - 12$ .

Factor $2$ out of $2 x$ .

$f (\frac{2 x - 12}{3}) = \frac{3}{2} \cdot \frac{2 (x) - 12}{3} - 6$

Factor $2$ out of $- 12$ .

$f (\frac{2 x - 12}{3}) = \frac{3}{2} \cdot \frac{2 x + 2 \cdot - 6}{3} - 6$

Factor $2$ out of $2 x + 2 \cdot - 6$ .

$f (\frac{2 x - 12}{3}) = \frac{3}{2} \cdot \frac{2 (x - 6)}{3} - 6$

Cancel the common factor of $3$ .

Cancel the common factor.

$f (\frac{2 x - 12}{3}) = \frac{3}{2} \cdot \frac{2 (x - 6)}{3} - 6$

Rewrite the expression.

$f (\frac{2 x - 12}{3}) = \frac{1}{2} \cdot (2 (x - 6)) - 6$

Cancel the common factor of $2$ .

Cancel the common factor.

$f (\frac{2 x - 12}{3}) = \frac{1}{2} \cdot (2 (x - 6)) - 6$

Rewrite the expression.

$f (\frac{2 x - 12}{3}) = x - 6 - 6$

Step 4

Subtract $6$ from $- 6$ .

$f (\frac{2 x - 12}{3}) = x - 12$