# How do you find the domain of y=(2x)/(-x-5)?

Mar 9, 2017

$\left\{x : x \in \mathbb{R} , x \ne - 5\right\}$

#### Explanation:

The domain of a function is all real values that x can have without causing the function to be undefined.

Here y will be undefined if the denominator equals zero.

$\Rightarrow - x - 5 = 0 \Rightarrow - x = 5 \Rightarrow x = - 5$

Hence the domain is ALL real values of x except x ≠ -5

Which may be expressed in $\textcolor{b l u e}{\text{set builder notation}}$ as

$\left\{x : x \in \mathbb{R} , x \ne - 5\right\}$