# How do you find the domain of f(x)=(x-2)/(x+4) ?

Jul 12, 2015

The only restriction on the domain comes from the $\left(x + 4\right)$ denominator, which cannot be zero.

So the domain is $\mathbb{R}$ \ $\left\{- 4\right\}$.

In interval notation: $\left(- \infty , - 4\right) \cup \left(- 4 , \infty\right)$

#### Explanation:

$\left(x - 2\right)$ is well defined for all $x \in \mathbb{R}$

$\left(x + 4\right)$ is well defined for all $x \in \mathbb{R}$

So $f \left(x\right) = \frac{x - 2}{x + 4}$ is well defined,

except when the denominator $\left(x + 4\right) = 0$,
which happens when $x = - 4$.