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

$x=\frac{π}{4},-\frac{π}{4}$ and 0 $x=\frac{π}{3},-\frac{π}{3}$ and 0 x = tan 1, −tan 1 and 0 none of these

x = tan 1, −tan 1 and 0

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.