At which points is the function f(x) = frac{x | vedclass

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(B) The function $f(x) = \frac{x}{[x]}$ is defined only when $[x] 
eq 0$.$(i)$ For $0 \le x < 1$,$[x] = 0$,so $f(x)$ is undefined in the interval $(0

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All positive and negative integers and $(0, 1)$

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(B) The function $f(x) = \frac{x}{[x]}$ is defined only when $[x] 
eq 0$.$(i)$ For $0 \le x $(ii)$ At any integer $n \in \mathbb{Z} \setminus \{0, 1\}$,the left-hand limit is $\lim_{x 	o n^-} \frac{x}{[x]} = \frac{n}{n-1}$ and the right-hand limit is $\lim_{x 	o n^+} \frac{x}{[x]} = \frac{n}{n} = 1$. Since $\frac{n}{n-1} 
eq 1$ for $n 
eq 0$,the function is discontinuous at all integers.$(iii)$ At $x = 1$,$\lim_{x 	o 1^-} f(x)$ is undefined (as $[x]=0$ for $x \in [0, 1)$),and $\lim_{x 	o 1^+} f(x) = 1$. Thus,it is discontinuous at $x = 1$.Hence,the function is discontinuous at all integers and in the interval $(0, 1)$.

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

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