As #y=arctanx# is the inverse of #y=tanx# 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=tanx# as you'd have an infinite number of #x != 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 RR# 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 RR# since the range of #tan# is that. Howerver it is impossible to define the range of #y=arctanx# since you'd have to have an infinite number of exceptions.