# How do you find the domain of f(x) = (x+2)/(x-3) ?

Jun 7, 2016

Domain = $\left\{x : x \epsilon \mathbb{R} , x \ne 3\right\}$

This reads as "The domain is the set of all elements x, such that x is an element of the set of Real numbers, but x is not equal to 3"

#### Explanation:

The domain is the set of all the possible x-values.

Looking at the numerator, any $x -$value can be used.

However, in a fraction the denominator may not be equal to 0.

In this case is $x = 3$, then the denominator will be 0, so $x$ may not be 3, but any other value would be fine. We write it as:

Domain = $\left\{x : x \epsilon \mathbb{R} , x \ne 3\right\}$

This reads as "The domain is the set of all elements x, such that x is an element of the set of Real numbers, but x is not equal to 3"