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If \( f: R \rightarrow R \) is a function defined by \( f(x)=[x] \cos \left(\frac{2 x-1}{2}\right) \pi \), where \( [x] \) denotes the greatest integer function, then \( f \) is :
(1) continuous for every real \( x \).
\( \mathrm{P} \)
(2) discontinuous only at \( x=0 \).
W
(3) discontinuous only at non-zero integral values of \( x \).
_ (4) continuous only at \( x=0 \).
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