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If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ is a function defined by $f(x)=[\mathrm{x}] \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\mathrm{x}]$ denotes the greatest integer function, then $f$ is
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continuous for every real $x$
continuous for every real $x$
$f(x)=[x] \cos \left(\frac{2 x-1}{2}\right) \pi=[x] \cos \left(x-\frac{1}{2}\right) \pi$
$=[x] \sin \pi x$ is continuous for every real $x$.
$=[x] \sin \pi x$ is continuous for every real $x$.
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