Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=\left|x^3-3 x\right|[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$. Which one of the following statements is TRUE?

• Correct answer
  A

  Every non-zero integer is a point of discontinuity of $f$
• B

  $f$ is continuous at every real number
• C

  Every integer is a point of discontinuity of $f$
• D

  $f$ is continuous at every real number except for $0, \pm \sqrt{3}$

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