Question

Range of coses^-1 x is

A. \((\frac{-\pi}{2},\frac{\pi}{2})\)

B. \([\frac{-\pi}{2},\frac{\pi}{2}]\)

C. \([\frac{-\pi}{2},\frac{\pi}{2}]\) - {0}

D. none of these

Answer 1

Correct Answer is (C)   \([\frac{-\pi}{2},\frac{\pi}{2}]\) - {0}

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

The graph of the function y =  cosec^-1(x) can be obtained from the graph of 

Y = cosec x by interchanging x and y axes.i.e, if (a,b) is a point on Y = cosec x then (b,a) is the point on the function y =  cosec^-1(x)

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

From the graph it is clear that the range of  cosec^-1​​​​​​​(x) is restricted to interval

 \([\frac{-\pi}{2},\frac{\pi}{2}]\) - {0}