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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Add $- 3$ and $3$ .

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

Add $x$ and $0$ .

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