At which points the function $f(x)=\frac{x}{[x]}$, where [.] is greatest integer function, is discontinuous

only positive integers all integer and (0, 1) all rational numbers none of these

all integer and (0, 1)

(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)