# How do you find the domain of f(x)=(x-3)/(x+4)?

Apr 13, 2018

Domain is all real numbers except $x = - 4$

#### Explanation:

The only limitation on the domain in this equation is undefined answers. Therefore, the limitation can be described by (denominator)=0 or in this case $x + 4 = 0$, so $x$ cannot equal $- 4$.

Apr 13, 2018

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

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) 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{(x-3)/(x+4) [-10, 10, -5, 5]}