At which points the function $f(x)=\frac{x}{[x]}$, where [.] is greatest integer function, is discontinuous
Answer & explanation
Correct answer: option 2
(i) When 0 ≤ x < 1
f(x) doesn’t exist as [x] = 0 here.
(ii) Also $\underset{x→I+}{\lim}f(x)$ and $\underset{x→I-}{\lim}f(x)$ does not exist.
Hence f(x) is discontinuous at all integers and also in (0, 1)