Algebra Examples

$f (x) = \frac{x - 8}{10}$ , $g (x) = 10 x + 8$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (10 x + 8)$ by substituting in the value of $g$ into $f$ .

$f (10 x + 8) = \frac{(10 x + 8) - 8}{10}$

Step 3

Cancel the common factor of $(10 x + 8) - 8$ and $10$ .

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Step 3.1

Factor $2$ out of $10 x$ .

$f (10 x + 8) = \frac{2 (5 x) + 8 - 8}{10}$

Step 3.2

Factor $2$ out of $8$ .

$f (10 x + 8) = \frac{2 (5 x) + 2 (4) - 8}{10}$

Step 3.3

Factor $2$ out of $2 (5 x) + 2 (4)$ .

$f (10 x + 8) = \frac{2 (5 x + 4) - 8}{10}$

Step 3.4

Factor $2$ out of $- 8$ .

$f (10 x + 8) = \frac{2 (5 x + 4) + 2 (- 4)}{10}$

Step 3.5

Factor $2$ out of $2 (5 x + 4) + 2 (- 4)$ .

$f (10 x + 8) = \frac{2 (5 x + 4 - 4)}{10}$

Step 3.6

Cancel the common factors.

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Step 3.6.1

Factor $2$ out of $10$ .

$f (10 x + 8) = \frac{2 (5 x + 4 - 4)}{2 (5)}$

Step 3.6.2

Cancel the common factor.

$f (10 x + 8) = \frac{2 (5 x + 4 - 4)}{2 \cdot 5}$

Step 3.6.3

Rewrite the expression.

$f (10 x + 8) = \frac{5 x + 4 - 4}{5}$

Step 4

Simplify the numerator.

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Step 4.1

Subtract $4$ from $4$ .

$f (10 x + 8) = \frac{5 x + 0}{5}$

Step 4.2

Add $5 x$ and $0$ .

$f (10 x + 8) = \frac{5 x}{5}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$f (10 x + 8) = \frac{5 x}{5}$

Step 5.2

Divide $x$ by $1$ .

$f (10 x + 8) = x$