# How do you find the domain of  f(x)= (x-2) /( x+3)?

Nov 25, 2017

The domain of $f \left(x\right)$ is $\mathbb{R} - \left\{- 3\right\}$

#### Explanation:

As you cannot divide by $0$, the denominator must be $\ne 0$

Therefore,

$x + 3 \ne 0$

$x \ne - 3$

The domain of $f \left(x\right)$ is $\mathbb{R} - \left\{- 3\right\}$

graph{(x-2)/(x+3) [-10, 10, -5, 5]}

Nov 25, 2017

$x \in \mathbb{R} , x \ne - 3$

#### Explanation:

$\text{the denominator of f(x) cannot be zero as this}$
$\text{would make f(x) undefined}$

$\text{equating the denominator to zero and solving}$
$\text{gives the value that x cannot be}$

$\text{solve "x+3=0rArrx=-3larrcolor(red)"excluded value}$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ne - 3$