Find f(g(x)) f(x)=2x-9 , g(x)=(x+2)/9

$f (x) = 2 x - 9$ , $g (x) = \frac{x + 2}{9}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 2}{9})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 2}{9}) = 2 (\frac{x + 2}{9}) - 9$

Step 3

Combine $2$ and $\frac{x + 2}{9}$ .

$f (\frac{x + 2}{9}) = \frac{2 (x + 2)}{9} - 9$

Step 4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$f (\frac{x + 2}{9}) = \frac{2 (x + 2)}{9} - 9 \cdot \frac{9}{9}$

Step 5

Simplify terms.

Combine $- 9$ and $\frac{9}{9}$ .

$f (\frac{x + 2}{9}) = \frac{2 (x + 2)}{9} + \frac{- 9 \cdot 9}{9}$

Combine the numerators over the common denominator.

$f (\frac{x + 2}{9}) = \frac{2 (x + 2) - 9 \cdot 9}{9}$

Step 6

Simplify the numerator.

Apply the distributive property.

$f (\frac{x + 2}{9}) = \frac{2 x + 2 \cdot 2 - 9 \cdot 9}{9}$

Multiply $2$ by $2$ .

$f (\frac{x + 2}{9}) = \frac{2 x + 4 - 9 \cdot 9}{9}$

Multiply $- 9$ by $9$ .

$f (\frac{x + 2}{9}) = \frac{2 x + 4 - 81}{9}$

Subtract $81$ from $4$ .

$f (\frac{x + 2}{9}) = \frac{2 x - 77}{9}$