question_answer

Function \[f(x)=x-[\,],\] where [ ] shows a greatest integer. This function is                                         [DCE 2005]

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

Correct Answer: C

Solution :

           It is well known fact that fractional function always a periodic function whose period is 1.                    \[-3\le x<-2,-2\le x<-1,-1\le x<0\]                    \[y=f(x),\,\,\,0,\le x+3<1,\,\,\,0\le x+2<1\],                    \[0\le x+1<1\]                    \[0\le x<1,\,\,1\le x<2\]                    \[0\le x<1,\,\,0\le x-1\le 1\].