Answer :

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


().

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