JEE Main 1989 Mathematics question on Limits Continuity and Differentiability

1. A.
   $\tan[f(x)]$ and $1/f(x)$ are both continuous
2. B.
   $\tan[f(x)]$ and $1/f(x)$ are both discontinuous
3. C.
   $\tan[f(x)]$ and $f^{-1}(x)$ are both continuous
4. D.
   $\tan[f(x)]$ is continuous but $1/f(x)$ is not continuous

[1989]