Precalculus Examples

$f (x) = \frac{\sqrt{x - 2}}{x - 5}$

Step 1

Set the radicand in $\sqrt{x - 2}$ greater than or equal to $0$ to find where the expression is defined.

$x - 2 \geq 0$

Step 2

Add $2$ to both sides of the inequality.

$x \geq 2$

Step 3

Set the denominator in $\frac{\sqrt{x - 2}}{x - 5}$ equal to $0$ to find where the expression is undefined.

$x - 5 = 0$

Step 4

Add $5$ to both sides of the equation.

$x = 5$

Step 5

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

Interval Notation:

$[2, 5) \cup (5, \infty)$

Set-Builder Notation:

${x | x \geq 2, x \neq 5}$

Step 6