# How do you find the domain of y =(8-x) /( x+4)?

Jul 9, 2018

$x \in \mathbb{R} , x \ne - 4$

#### Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

$\text{solve "x+4=0rArrx=-4larrcolor(red)"excluded value}$

$\text{domain is } x \in \mathbb{R} , x \ne - 4$

$x \in \left(- \infty , - 4\right) \cup \left(- 4 , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$
graph{(8-x)/(x+4) [-10, 10, -5, 5]}