Find f(g(x)) f(x)=(x-5)/2 g(x)=2x-5

$f (x) = \frac{x - 5}{2}$ $g (x) = 2 x - 5$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x - 5)$ by substituting in the value of $g$ into $f$ .

$f (2 x - 5) = \frac{(2 x - 5) - 5}{2}$

Step 3

Simplify the numerator.

Subtract $5$ from $- 5$ .

$f (2 x - 5) = \frac{2 x - 10}{2}$

Factor $2$ out of $2 x - 10$ .

Factor $2$ out of $2 x$ .

$f (2 x - 5) = \frac{2 (x) - 10}{2}$

Factor $2$ out of $- 10$ .

$f (2 x - 5) = \frac{2 x + 2 \cdot - 5}{2}$

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$f (2 x - 5) = \frac{2 (x - 5)}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$f (2 x - 5) = \frac{2 (x - 5)}{2}$

Divide $x - 5$ by $1$ .

$f (2 x - 5) = x - 5$