Find g(f(x)) f(x)=5x-5 , g(x)=(x+5)/5

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Cancel the common factor of $(5 x - 5) + 5$ and $5$ .

Factor $5$ out of $5 x$ .

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

Factor $5$ out of $- 5$ .

$g (5 x - 5) = \frac{5 (x) + 5 \cdot - 1 + 5}{5}$

Factor $5$ out of $5 (x) + 5 (- 1)$ .

$g (5 x - 5) = \frac{5 (x - 1) + 5}{5}$

Factor $5$ out of $5$ .

$g (5 x - 5) = \frac{5 (x - 1) + 5 \cdot 1}{5}$

Factor $5$ out of $5 (x - 1) + 5 (1)$ .

$g (5 x - 5) = \frac{5 (x - 1 + 1)}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$g (5 x - 5) = \frac{5 (x - 1 + 1)}{5 (1)}$

Cancel the common factor.

$g (5 x - 5) = \frac{5 (x - 1 + 1)}{5 \cdot 1}$

Rewrite the expression.

$g (5 x - 5) = \frac{x - 1 + 1}{1}$

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

$g (5 x - 5) = x - 1 + 1$

Step 4

Combine the opposite terms in $x - 1 + 1$ .

Add $- 1$ and $1$ .

$g (5 x - 5) = x + 0$

Add $x$ and $0$ .

$g (5 x - 5) = x$