Period of f(x) = nx + n - [nx + n] , n ∈ N where [ ] denotes greatest integer function is :

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1.Relation and Function

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Period of $f(x) = nx + n - [nx + n]$, $n \in N$

where [ ] denotes the greatest integer function is :

A

$1$

B

$1/n$

C

$n$

D

none of these

Solution

$f(x)=n x+n-[n x+n]$

$f(x)=\{n x+n\}=\{n(x+1)\}$ where $\{\cdot\}$ is fractional function which has period value of 1

Therefore, period will be $\frac{1}{n}$

Standard 12

Mathematics

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