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+2 votes
5.3k views
in Trigonometry by (25.8k points)
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Range of sec-1 x is

A. \([0,\frac{\pi}{2}]\)

B. [0, π]

C. \([0, \pi]-\{\frac{\pi}{2}\}\)

D. none of these

1 Answer

+2 votes
by (27.7k points)
selected by
 
Best answer

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

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

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

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

Below is the Graph of the range of  sec-1(x) 

From the graph, it is clear that the range of sec-1(x)  is restricted to interval

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

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