Question

Which among the following represents the graph of $y=se{c}^{-1}\left(x\right)$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The question in hand is to find the graph $se{c}^{-1}\left(x\right)$
First of all keep in mind the domain and range of the function $se{c}^{-1}\left(x\right)$. Its domain is R-(-1,1) and range $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$
since $sec\theta$ is not defined at the point $x=\frac{\pi }{2}$. There is only one curve which satisfies this domain and range which is option (d). Note the endpoints of the curve (-1, $\pi$) and (1, 0). Also try to identify which functions are related to other options.
Option (a) has the graph of $y=si{n}^{-1}\left(x\right)$
Option (b) has $y=ta{n}^{-1}\left(x\right)$
Option (c) has $y=cose{c}^{-1}\left(x\right)$