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

A

continuous for every real $$x$$

B

discontinuous only at $$x = 0$$

C

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

D

continuous only at $$x = 0$$