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

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

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 $f$ .

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Combine the opposite terms in $x + 2 - 2$ .

Subtract $2$ from $2$ .

$f (\frac{x + 2}{3}) = x + 0$

Add $x$ and $0$ .

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