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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify the numerator.

Subtract $1$ from $- 1$ .

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

Factor $2$ out of $2 x - 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 2$ .

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

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

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x - 1$ by $1$ .

$f (2 x - 1) = x - 1$