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.

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