Linear Algebra Examples

$f (x) = \frac{x^{3} - x^{2} + 1}{| x |}$

Step 1

Set the denominator in $\frac{x^{3} - x^{2} + 1}{| x |}$ equal to $0$ to find where the expression is undefined.

$| x | = 0$

Step 2

Solve for $x$ .

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Step 2.1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm 0$

Step 2.2

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 4