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

$\tan f\left(x\right) \text{and }\frac{1}{f\left(x\right)}$ are continuous

$\tan f\left(x\right) \text{and }\frac{1}{f\left(x\right)}$ are discontinuous

$\tan f\left(x\right) \text{and }\frac{1}{f^{-1}\left(x\right)}$ are continuous

$\tan f\left(x\right)$ is not continuous but $\frac{1}{f\left(x\right)}$ is continuous