Precalculus Examples

$f (x) = \frac{x - 2}{x^{4} - 16}$

Step 1

Set the denominator in

$\frac{x - 2}{x^{4} - 16}$ equal to

$0$ to find where the expression is undefined.

$x^{4} - 16 = 0$

Step 2

Solve for

$x$ .

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Step 2.1

Add

$16$ to both sides of the equation.

$x^{4} = 16$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{16}$

Step 2.3

Simplify

$\pm \sqrt[4]{16}$ .

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Step 2.3.1

Rewrite

$16$ as

$2^{4}$ .

$x = \pm \sqrt[4]{2^{4}}$

Step 2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

Step 2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.4.1

First, use the positive value of the

$\pm$ to find the first solution.

$x = 2$

Step 2.4.2

Next, use the negative value of the

$\pm$ to find the second solution.

$x = - 2$

Step 2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$

Step 3

The domain is all values of

$x$ that make the expression defined.

Interval Notation:

$(- \infty, - 2) \cup (- 2, 2) \cup (2, \infty)$

Set-Builder Notation:

${x | x \neq 2, - 2}$

Step 4

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