If $f(x)=\large\frac{x}{2}$$-1$, then on the interval $[0,\pi]$

Question

$\begin{array}{1 1}(a)\;\tan[f(x)]\;and \;1/f(x)\;are\;both\;continuous\\(b)\;\tan[f(x)]\;and \;1/f(x)\;are\;both\;discontinuous\\(c)\;\tan[f(x)]\;and \;f^{-1}(x)\;are\;both\;continuous\\(d)\;\tan[f(x)]\;is\; continuous\;but\;1/f(x)\;is\;not\end{array}$