# How do you find the domain and range of tan^-1(x)?

Jul 30, 2018

#### Answer:

The domain is $x \in \mathbb{R}$. The range is $y \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$

#### Explanation:

Before let's define the domain and range of

$y = \tan x$

The domain of the function $y = \tan x$ is

$x \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$

The range of the function $y = \tan x$ is

$y \in \left(- \infty , + \infty\right)$

The function $y = {\tan}^{-} 1 x$ is symmetric to the function $y = \tan x$ with respect the line $y = x$

Therefore, the domain is $x \in \mathbb{R}$

and the range is $y \in \left(- \frac{\pi}{2} , \frac{\pi}{2}\right)$

graph{(y-tanx)(y-arctanx)(y-x)=0 [-5.014, 9.034, -3.367, 3.66]}