$f(x)=[\tan^{-1}x]$, where [.] denotes the greatest integer function, is discontinuous at
Answer & explanation
Correct answer: option 3
f(x) will be discontinuous when $tan^{−1}x = 0$, 1, −1 as $tan^{−1}x\left(-\frac{π}{2},\frac{π}{2}\right)∀x∈(-∞,∞)$.
Thus f(x) is discontinuous at x = 0, tan 1, −tan 1.