Precalculus Examples

$f (x) = \frac{x}{x + 1}$ , $g (x) = \frac{8}{x}$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(\frac{x}{x + 1}) \cdot (\frac{8}{x})$

Step 1.2

Simplify.

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Step 1.2.1

Cancel the common factor of $x$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{x}{x + 1} \cdot \frac{8}{x}$

Step 1.2.1.2

Rewrite the expression.

$\frac{1}{x + 1} \cdot 8$

Step 1.2.2

Combine $\frac{1}{x + 1}$ and $8$ .

$\frac{8}{x + 1}$

Step 2

Set the denominator in $\frac{8}{x + 1}$ equal to $0$ to find where the expression is undefined.

$x + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 1) \cup (- 1, \infty)$

Set-Builder Notation:

${x | x \neq - 1}$

Step 5