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If \mathrm{f(x)=\cos ^{-1}(\cos x)}  then \mathrm{f(x)}  is
 

Option: 1

 continuous at \mathrm{ x=\pi}
 


Option: 2

 discontinuous at \mathrm{x=-\pi}
 


Option: 3

differentiable at \mathrm{x=0}
 


Option: 4

 nondifferentiable at \mathrm{x=\pi / 2}


Answers (1)

best_answer

Here, 

\begin{aligned} \mathrm{f(x)=\cos ^{-1}(\cos x)}&=\mathrm{2 \pi+x,-2 \pi<x<-\pi}\\ & \mathrm{-x,-\pi \leq x<0} \\ & \mathrm{x, 0 \leq x \leq \pi }\\ & \mathrm{2 \pi-x, \pi<x<2 \pi .} \end{aligned}
Use these definitions for selecting the options.

Posted by

Rishi

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