To Find: The range of tan^-1 x

Here,the inverse function is given by y =

The graph of the function y = can be obtained from the graph of

Y = tan x by interchanging x and y axes.i.e, if (a,b) is a point on Y = tan x then (b,a) is the point on the function y =

Below is the Graph of the range of

From the graph, it is clear that the range of is restricted to any of the intervals like [] , [] , [] and so on. Hence the range is given by

().