The correct option is D f is continuous everywhere
We have
f(x)=|sin x|We know that |x| and sinx are continuous everywhere.
Hence, |sin x| is continuous everywhere for all x.
|x| is non-differentiable at x=0.
Therefore, |sinx| is non-differentiable at x=0.
So, |sinx| is non-differentiable when sinx=0, or x=nπ,n∈Z.
Hence, f(x) is continuous everywhere but not differentiable at x=nπ,n∈Z