Precalculus Examples

$\frac{\sqrt{x} - 3}{x - 9}$

Step 1

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

$x \geq 0$

Step 2

Set the denominator in $\frac{\sqrt{x} - 3}{x - 9}$ equal to $0$ to find where the expression is undefined.

$x - 9 = 0$

Step 3

Add $9$ to both sides of the equation.

$x = 9$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

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

Step 5