If $[x]$ is the greatest integer function and $f(x)= \begin{cases}2[x]-\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{cases}$ is a real valued function, then $f$ is

• A

  continuous at $x=0$
• B

  continuous at $x=1$
• C

  left continuous at $x=0$
• Correct answer
  D

  right continuous at $x=1$

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