The period of f(x) = x - [x],if it is periodi | vedclass

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(C) Let $f(x)$ be a periodic function with period $T > 0$.Then,by definition,$f(x + T) = f(x)$ for all $x \in \mathbb{R}$.Substituting the given funct

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$1$

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(C) Let $f(x)$ be a periodic function with period $T > 0$.Then,by definition,$f(x + T) = f(x)$ for all $x \in \mathbb{R}$.Substituting the given function $f(x) = x - [x]$:$(x + T) - [x + T] = x - [x]$$x + T - [x + T] = x - [x]$$T = [x + T] - [x]$For this equation to hold for all $x \in \mathbb{R}$,$T$ must be an integer.The smallest positive value of $T$ that satisfies this condition is $T = 1$.Therefore,the period of the function $f(x) = x - [x]$ (which is the fractional part function ${x}$) is $1$.

The period of $f(x) = x - [x]$,if it is periodic,is

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