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

Question

( A ) continuous for every real $x$
( B ) continuous only at $x=0$
( C ) discontinuous only at $x=0$
( D ) discontinuous only at non-zero integral values of $x$