Mathematics Differential Calculus Differentiability

Let \(K\) be the set of all real values of \(x\) where the function \(f(x)=\sin |x|-|x|+2(x- \pi)\cos|x|\) is not differentiable. Then the set \(K\) is equal to:

1
\(\{\pi\}\)
2
\(\{0\}\)
3
\(\phi \,(\text{an empty set})\)
4
\(\{0,\pi\}\)

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