What is the domain of arctan(x)?

1 Answer
Mar 28, 2016

The domain of arctan(x) is the whole of RR, that is: (-oo, oo)

Explanation:

The function tan(x) is a many to one periodic function, so to define an inverse function requires that we restrict its domain (or restrict the range of the inverse function).

To define arctan(x) as a function we can restrict the domain of tan(x) to (-pi/2, pi/2). The function tan(x) is one to one, continuous and unbounded over this interval, so has a well defined inverse arctan(x): RR -> (-pi/2, pi/2) that is also continuous and one to one.