If \( f(x)=\cos \pi(|x|+[x]) \), then \( f \) is (where \( [\cdot] \) denotes greatest integral ...

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If \( f(x)=\cos \pi(|x|+[x]) \), then \( f \) is (where \( [\cdot] \) denotes greatest integral function), then which is not true?
(A) Continuous at \( x=1 / 2 \)
(B) Continuous at \( x=0 \)
(C) Differentiable in \( (-1,0) \)
(D) Differentiable in \( (0,1) \)
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