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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Combine the opposite terms in $x - 3 + 3$ .

Add $- 3$ and $3$ .

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

Add $x$ and $0$ .

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