If $f(x) = \frac{x}{2} - 1$,then on the interval $[0, \pi]$,where $[.]$ represents the greatest integer function,which of the following is true?

• A
  $\tan [f(x)]$ is continuous but $\frac{1}{f(x)}$ is not continuous.
• B
  $\tan [f(x)]$ and $\frac{1}{f(x)}$ are both continuous.
• C
  $\tan [f(x)]$ and $\frac{1}{f(x)}$ are both discontinuous.
• D
  $\tan [f(x)]$ is discontinuous and $\frac{1}{f(x)}$ is continuous.