question_answer

If \[f(x)=\max ,(\sin x,{{\sin }^{-1}}(\cos x))\], then

A)  \[f\] is differentiable every where

B)  \[f\] is continuous every where but not differentiable

C) \[f\] is discontinuous at \[x=\frac{n\pi }{2},n\in I\]

D)  \[f\] is non-differentiable at \[x=\frac{n\pi }{2},n\in I\]

Correct Answer: B

Solution :

\[f(x)=\max .\{\sin x,{{\sin }^{-1}}(\cos x)\}\] Clearly, f(x) is continuous but non-differentiable at infinite points.