JEE Math Practice 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

1. A.continuous for every real $$x$$
2. B.discontinuous only at $$x=0$$
3. C.discontinuous only at non-zero integral values of $$x$$
4. D.continuous only at $$x=0$$