If f: R rightarrow R is defined by f(x) = x - | vedclass

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(C) The function $f(x) = x - [x]$ is the fractional part function,denoted as $\{x\}$.We check the continuity of $f(x)$ at any integer $n \in Z$.The le

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$Z$

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(C) The function $f(x) = x - [x]$ is the fractional part function,denoted as $\{x\}$.We check the continuity of $f(x)$ at any integer $n \in Z$.The left-hand limit at $x = n$ is:$\lim_{x \rightarrow n^-} f(x) = \lim_{h \rightarrow 0} (n - h - [n - h]) = \lim_{h \rightarrow 0} (n - h - (n - 1)) = \lim_{h \rightarrow 0} (1 - h) = 1$.The right-hand limit at $x = n$ is:$\lim_{x \rightarrow n^+} f(x) = \lim_{h \rightarrow 0} (n + h - [n + h]) = \lim_{h \rightarrow 0} (n + h - n) = \lim_{h \rightarrow 0} h = 0$.The value of the function at $x = n$ is:$f(n) = n - [n] = n - n = 0$.Since the left-hand limit $(1)$ is not equal to the right-hand limit $(0)$,the function $f(x)$ is discontinuous at every integer $n \in Z$.Therefore,the set of points of discontinuity is $Z$.

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is

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