Find g(f(x)) f(x)=4x-2 , g(x)=(x+4)/2

$f (x) = 4 x - 2$ , $g (x) = \frac{x + 4}{2}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (4 x - 2)$ by substituting in the value of $f$ into $g$ .

$g (4 x - 2) = \frac{(4 x - 2) + 4}{2}$

Step 3

Cancel the common factor of $(4 x - 2) + 4$ and $2$ .

Factor $2$ out of $4 x$ .

$g (4 x - 2) = \frac{2 (2 x) - 2 + 4}{2}$

Factor $2$ out of $- 2$ .

$g (4 x - 2) = \frac{2 (2 x) + 2 \cdot - 1 + 4}{2}$

Factor $2$ out of $2 (2 x) + 2 (- 1)$ .

$g (4 x - 2) = \frac{2 (2 x - 1) + 4}{2}$

Factor $2$ out of $4$ .

$g (4 x - 2) = \frac{2 (2 x - 1) + 2 \cdot 2}{2}$

Factor $2$ out of $2 (2 x - 1) + 2 (2)$ .

$g (4 x - 2) = \frac{2 (2 x - 1 + 2)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$g (4 x - 2) = \frac{2 (2 x - 1 + 2)}{2 (1)}$

Cancel the common factor.

$g (4 x - 2) = \frac{2 (2 x - 1 + 2)}{2 \cdot 1}$

Rewrite the expression.

$g (4 x - 2) = \frac{2 x - 1 + 2}{1}$

Divide $2 x - 1 + 2$ by $1$ .

$g (4 x - 2) = 2 x - 1 + 2$

Step 4

Add $- 1$ and $2$ .

$g (4 x - 2) = 2 x + 1$