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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Combine $2$ and $\frac{x + 2}{3}$ .

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

Step 4

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

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

Step 5

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $2$ .

$f (\frac{x + 2}{3}) = \frac{2 x + 4 - 3 \cdot 3}{3}$

Multiply $- 3$ by $3$ .

$f (\frac{x + 2}{3}) = \frac{2 x + 4 - 9}{3}$

Subtract $9$ from $4$ .

$f (\frac{x + 2}{3}) = \frac{2 x - 5}{3}$