Question

Range of tan ^-1 x is

A. \((0,\frac{\pi}{2})\)

B. \((\frac{-\pi}{2},\frac{\pi}{2})\)

C. \([\frac{-\pi}{2},\frac{\pi}{2}]\)

D. none of these

Answer 1

Correct Answer is (B) \((\frac{-\pi}{2},\frac{\pi}{2})\)

Here,the inverse function is given by y = f^-1 (x) 

The graph of the function y = tan^-1 (x) 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 = tan^-1 (x) 

Below is the Graph of the range of tan^-1 (x)

From the graph, it is clear that the range of tan^-1 (x) is restricted to any of the intervals like \([\frac{3\pi}{2},\frac{\pi}{2}]\) , \([\frac{-\pi}{2},\frac{\pi}{2}]\) ,\([\frac{\pi}{2},\frac{3\pi}{2}]\)and so on. Hence the range is given by

\((\frac{-\pi}{2},\frac{\pi}{2})\)