If $f:R \to R$ is a function defined by $f\left( x \right) = \left[ x \right]\cos \left( {{{2x - 1} \over 2}} \right)\pi $, where [x] denotes the greatest integer function, then $f$ is

Question

If $f:R \to R$ is a function defined by

$f\left( x \right) = \left[ x \right]\cos \left( {{{2x - 1} \over 2}} \right)\pi $,

where [x] denotes the greatest integer function, then $f$ is

continuous for every real $x$

discontinuous only at $x=0$

discontinuous only at non-zero integral values of $x$

continuous only at $x=0$

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