Mark the tick against the correct answer in the following: Range of $\sec ^{-1} x$ is A. $\left[0, \frac{\pi}{2}\right]$ B. $[0, \pi]$ C. $[0, \pi]-\left\{\frac{\pi}{2}\right\}$ D. None of these

Home » Mark the tick against the correct answer in the following: Range of is A. B. C. D. None of these

Mark the tick against the correct answer in the following: Range of $\sec ^{-1} x$ is
A. $\left[0, \frac{\pi}{2}\right]$
B. $[0, \pi]$
C. $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
D. None of these

CBSE | Class 12 | Inverse Trigonometric Functions | Maths | RS Aggarwal

Mark the tick against the correct answer in the following: Range of $\sec ^{-1} x$ is
A. $\left[0, \frac{\pi}{2}\right]$
B. $[0, \pi]$
C. $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
D. None of these

Solution:

Option(C) is correct.
To Find:The range of $\sec ^{-1}(x)$
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 $\sec ^{-1}(x)$