Question

If $f\left(x\right)={\cos }^{-1}\left(\cos x\right),$ then $f\left(x\right)$ is

• A. Discontinuous at $x=2\pi$
• B. Discontinuous at $x=\pi$
• C. Differentiable at $x=\pi$
• D. Non differentiable at $x=\pi$

Answer 1

The correct option is D Non differentiable at $x=\pi$


Clearly, from the graph of $f\left(x\right)={\cos }^{-1}\left(\cos x\right)$, we can observe that it is continuous throughout its domain.
But it has sharp edges at $x=n\pi ,n\in Z$. Hence it is non differentiable at these points.