The function $\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\cdot]$ denotes the greatest integer function, is discontinuous at

• A

  (A) all irrational numbers $x$.
• B

  no $x$.
• Correct answer
  C

  all integer points.
• D

  every rational $x$ which is not an integer.

Hence, the correct answer is option: 'C'.