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

May 28, 2017

Domain: $\left\{x | x \ne 2\right\}$

#### Explanation:

There are two ways you can impact the domain of a real-valued function. The first is plugging in any $x$ value that would cause you to divide by zero. The other is plugging in $x$ values that would cause an even root to be negative.

There are no square roots in this problem, but there is a fraction with $x$ in the denominator. So we need to find where the denominator is zero.

$x + 2 = 0$ whenever $x = - 2$

So, the domain is all values of $x$ except for $x = - 2$. This sentences is often written in mathematical short hand as

$\left\{x | x \ne 2\right\}$