# How do you find the domain & range for y=Arctan x?

As $y = \arctan x$ is the inverse of $y = \tan x$ it can't be done. As we know tan goes on forever but when working in degrees you can never input values of 90, 270 and so on. This makes it impossible to define a domain for $y = \tan x$ as you'd have an infinite number of $x \ne 90$ and so on exceptions.
Additonaly the range of $\tan$ goes on into infinity which makes it even more tricky. The range however can technically be defined as all real values of y: $y \in \mathbb{R}$ although its not good practice.
For these reasons it is not possible to define $\arctan$'s domain or range in a mathematically correct way however you can technically define its domain as all real values of x: $x \in \mathbb{R}$ since the range of $\tan$ is that. Howerver it is impossible to define the range of $y = \arctan x$ since you'd have to have an infinite number of exceptions.