For a real number $x$ let $[x]$ denote the largest number less than or equal to $x$. for $x \in R$ let $f(x)=[x] \sin \pi x$. Then:

• A

  $\mathrm{f}$ is differentiable on $\mathrm{R}$
• B

  $f$ is symmetric about the line $x=0$
• C

  $\int_{-3}^{3} f(x) d x=0$
• Correct answer
  D

  For each real $\alpha$, the equation $f(x)-\alpha=0$ has infinitely many roots.

Solution

$f(x)=[x] \sin \pi x$

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