Define a function $f(x)=\left\{\begin{array}{l}\sin x, \text { if } x \text { is irrational } \\ \tan x, \text { if } x \text { is rational. }\end{array}\right.$ Then $f(x)$ is

• A

  not continuous at any point of the interval $(-\pi, \pi)$.
• B

  continuous at some point(s), but not differentiable at any point of the interval $(-\pi, \pi)$.
• C

  continuous at some point(s) of the interval $(-\pi, \pi)$, but not differentiable at some of these point(s).
• Correct answer
  D

  continuous at some point(s) of the interval $(-\pi, \pi)$ and differentiable at all these point(s).

Hence, the correct answer is option: 'D'.