(C) The function $f(x) = x - [x]$ is known as the fractional part function,denoted by $\{x\}$.By definition,for any integer $n$,we have $[x + n] = [x]

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$A$ periodic function whose period is $1$

(C) The function $f(x) = x - [x]$ is known as the fractional part function,denoted by $\{x\}$.By definition,for any integer $n$,we have $[x + n] = [x] + n$.Therefore,$f(x + 1) = (x + 1) - [x + 1] = x + 1 - ([x] + 1) = x - [x] = f(x)$.Since $f(x + 1) = f(x)$ for all $x \in \mathbb{R}$,the function is periodic with period $1$.

Class 12 Mathematics Relation and Function Functional Equations

Easy

The function $f(x) = x - [x]$,where $[x]$ denotes the greatest integer function,is:

A
$A$ periodic function
B
$A$ periodic function whose period is $\frac{1}{2}$
C
$A$ periodic function whose period is $1$
D
Not a periodic function

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MediumWBJEE 2025

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EasyAP EAMCET 2022

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If $f(x)$ is a polynomial function satisfying $f(x) \cdot f(\frac{1}{x}) = f(x) + f(\frac{1}{x})$ and $f(4) = 65$,then the value of $f(6)$ is:

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The function $f(x) = x - [x]$,where $[x]$ denotes the greatest integer function,is:

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If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$,then $f(9)$ is equal to

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