Find f(g(x)) f(x)=2x+2 , g(x)=x/2-1

$f (x) = 2 x + 2$ , $g (x) = \frac{x}{2} - 1$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{x}{2} - 1)$ by substituting in the value of $g$ into $f$ .

$f (\frac{x}{2} - 1) = 2 (\frac{x}{2} - 1) + 2$

Simplify each term.

Apply the distributive property.

$f (\frac{x}{2} - 1) = 2 (\frac{x}{2}) + 2 \cdot - 1 + 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$f (\frac{x}{2} - 1) = 2 (\frac{x}{2}) + 2 \cdot - 1 + 2$

Rewrite the expression.

$f (\frac{x}{2} - 1) = x + 2 \cdot - 1 + 2$

Multiply $2$ by $- 1$ .

$f (\frac{x}{2} - 1) = x - 2 + 2$

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

Add $- 2$ and $2$ .

$f (\frac{x}{2} - 1) = x + 0$

Add $x$ and $0$ .

$f (\frac{x}{2} - 1) = x$