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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 l

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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 is:$\lim_{x ightarrow n^-} f(x) = \lim_{h ightarrow 0} f(n-h) = \lim_{h ightarrow 0} ((n-h) - [n-h]) = \lim_{h ightarrow 0} ((n-h) - (n-1)) = \lim_{h ightarrow 0} (1-h) = 1$.The right-hand limit is:$\lim_{x ightarrow n^+} f(x) = \lim_{h ightarrow 0} f(n+h) = \lim_{h ightarrow 0} ((n+h) - [n+h]) = \lim_{h ightarrow 0} ((n+h) - n) = \lim_{h ightarrow 0} h = 0$.The value of the function at $x=n$ is:$f(n) = n - [n] = n - n = 0$.Since $\lim_{x ightarrow n^-} f(x) 
eq \lim_{x ightarrow n^+} f(x)$, 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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