question_answer

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

A) f is differentiable everywhere                        

B) f is continuous everywhere 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 :

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