Mark the tick against the correct answer in the following: Domain of $\sec ^{-1} x$ is A. $[-1,1]$ B. $R-\{0\}$ C. $R-[-1,1]$ D. $R-\{-1,1\}$

Home » Mark the tick against the correct answer in the following: Domain of is A. B. C. D.

Mark the tick against the correct answer in the following: Domain of $\sec ^{-1} x$ is
A. $[-1,1]$
B. $R-\{0\}$
C. $R-[-1,1]$
D. $R-\{-1,1\}$

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

Mark the tick against the correct answer in the following: Domain of $\sec ^{-1} x$ is
A. $[-1,1]$
B. $R-\{0\}$
C. $R-[-1,1]$
D. $R-\{-1,1\}$

Solution:

Option(C) is correct.
To Find: The Domain 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 domain of $\sec ^{-1}(x)$
From the graph, it is clear that the domain of $\sec ^{-1}(x)$ is a set of all real numbers excluding $-1$ and 1 i.e, $\mathrm{R}$ $[-1,1]$