Precalculus Examples

$\frac{\sqrt{x + 4}}{x^{2}}$

Step 1

Set the radicand in $\sqrt{x + 4}$ greater than or equal to $0$ to find where the expression is defined.

$x + 4 \geq 0$

Step 2

Subtract $4$ from both sides of the inequality.

$x \geq - 4$

Step 3

Set the denominator in $\frac{\sqrt{x + 4}}{x^{2}}$ equal to $0$ to find where the expression is undefined.

$x^{2} = 0$

Step 4

Solve for $x$ .

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Step 4.1

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

$x = \pm \sqrt{0}$

Step 4.2

Simplify $\pm \sqrt{0}$ .

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Step 4.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 4.2.2

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

$x = \pm 0$

Step 4.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 5

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

Interval Notation:

$[- 4, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \geq - 4, x \neq 0}$

Step 6