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\mathrm{f(x)=\left[\tan ^{-1} x\right]}, where [.] denotes the greatest integer function, is discontinuous at

Option: 1

x=\frac{\pi}{4},-\frac{\pi}{4}\: and\: 0


Option: 2

x=\frac{\pi}{3},-\frac{\pi}{3}$ and $0


Option: 3

x=\tan 1,-\tan 1$ and $ 0


Option: 4

none of these


Answers (1)

best_answer

\mathrm{f\left ( x \right )} will be discontinuous when \mathrm{\tan ^{-1} x=0,1,-1} as

\mathrm{\tan ^{-1} x\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \quad \forall x \in(-\infty, \infty) \text { }}.
Thus \mathrm{f(x)} is discontinuous at \mathrm{x=0, \tan 1,-\tan 1}.

Posted by

Irshad Anwar

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