Question

Period of $f\left(x\right)=nx+n-[nx+n]$, $(nϵN$ where $\left[\right]$ denotes the greatest integer function is

• A. $1$
• B. $\frac{1}{n}$
• C. $n$
• D. none of these

Answer 1

The correct option is B $\frac{1}{n}$

$f\left(x\right)=nx+n-[nx+n]$
$f\left(x\right)=\{nx+n\}=\left\{n\right(x+1\left)\right\}$ where $\{\cdot \}$ is fractional function which has period value of $1$
Therefore, period will be $\frac{1}{n}$
Hence, option 'B' is correct.