If \( f: R \rightarrow R \) is a function define by \[ f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\rig...

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If \( f: R \rightarrow R \) is a function define by
\[
f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi
\]
where [路] denotes the greatest integer function, then \( f \) is
(a) Discontinuous at all integral values of \( x \) except at \( x=1 \)
(b) Continuous only at \( x=1 \)
(c) Continuous for every real \( x \)
(d) Discontinuous only at \( x=1 \)
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