Precalculus Examples

$y = \sqrt{x - 3} + \frac{1}{x - 3}$

Step 1

Set the radicand in $\sqrt{x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$x - 3 \geq 0$

Step 2

Add $3$ to both sides of the inequality.

$x \geq 3$

Step 3

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

$x - 3 = 0$

Step 4

Add $3$ to both sides of the equation.

$x = 3$

Step 5

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

Interval Notation:

$(3, \infty)$

Set-Builder Notation:

${x | x > 3}$

Step 6