Find g(f(x)) f(x)=10x+6 , g(x)=(x-6)/10

$f (x) = 10 x + 6$ , $g (x) = \frac{x - 6}{10}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (10 x + 6)$ by substituting in the value of $f$ into $g$ .

$g (10 x + 6) = \frac{(10 x + 6) - 6}{10}$

Step 3

Cancel the common factor of $(10 x + 6) - 6$ and $10$ .

Factor $2$ out of $10 x$ .

$g (10 x + 6) = \frac{2 (5 x) + 6 - 6}{10}$

Factor $2$ out of $6$ .

$g (10 x + 6) = \frac{2 (5 x) + 2 (3) - 6}{10}$

Factor $2$ out of $2 (5 x) + 2 (3)$ .

$g (10 x + 6) = \frac{2 (5 x + 3) - 6}{10}$

Factor $2$ out of $- 6$ .

$g (10 x + 6) = \frac{2 (5 x + 3) + 2 (- 3)}{10}$

Factor $2$ out of $2 (5 x + 3) + 2 (- 3)$ .

$g (10 x + 6) = \frac{2 (5 x + 3 - 3)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$g (10 x + 6) = \frac{2 (5 x + 3 - 3)}{2 (5)}$

Cancel the common factor.

$g (10 x + 6) = \frac{2 (5 x + 3 - 3)}{2 \cdot 5}$

Rewrite the expression.

$g (10 x + 6) = \frac{5 x + 3 - 3}{5}$

Step 4

Simplify the numerator.

Subtract $3$ from $3$ .

$g (10 x + 6) = \frac{5 x + 0}{5}$

Add $5 x$ and $0$ .

$g (10 x + 6) = \frac{5 x}{5}$

Step 5

Cancel the common factor of $5$ .

Cancel the common factor.

$g (10 x + 6) = \frac{5 x}{5}$

Divide $x$ by $1$ .

$g (10 x + 6) = x$