Question

Function$f\left(x\right)=x-\left[x\right]$ where [ ] shows a greatest integer. This function is

• A. A periodic function
• B. A periodic function whose period is1/2
• C. A periodic function whose period is 1
• D. Not a periodic function

Answer 1

The correct option is C A periodic function whose period is 1

It is well known fact that fractional function always a periodic function whose periods is 1.

$-3\le x<-2,-2\le x<-1,-1\le x<0$

$y=f\left(x\right),0\le x+3<1,0\le x+2<1,$

$0\le x+1<1$

$0\le x<1,1\le x<2$

$0\le x<1,0\le x-1\le 1.$