Precalculus Examples

$g (x) = \sqrt{x + 9} - \frac{1}{x}$

Step 1

Set the radicand in $\sqrt{x + 9}$ greater than or equal to $0$ to find where the expression is defined.

$x + 9 \geq 0$

Step 2

Subtract $9$ from both sides of the inequality.

$x \geq - 9$

Step 3

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

$x = 0$

Step 4

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

Interval Notation:

$[- 9, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \geq - 9, x \neq 0}$

Step 5