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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 2}{6})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Simplify terms.

Combine $- 6$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Multiply $- 6$ by $3$ .

$f (\frac{x + 2}{6}) = \frac{x + 2 - 18}{3}$

Subtract $18$ from $2$ .

$f (\frac{x + 2}{6}) = \frac{x - 16}{3}$