Precalculus Examples

\frac{1}{x - 2}

$\frac{1}{x - 2}$

Step 1

Set the denominator in

\frac{1}{x - 2}

$\frac{1}{x - 2}$ equal to

0

$0$ to find where the expression is undefined.

x - 2 = 0

$x - 2 = 0$

Step 2

Add

2

$2$ to both sides of the equation.

x = 2

$x = 2$

Step 3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

(- \infty, 2) \cup (2, \infty)

$(- \infty, 2) \cup (2, \infty)$

Set-Builder Notation:

{x | x \neq 2}

${x | x \neq 2}$

Step 4

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$