MCQ
Function $f(x) = x - [\,x],$ where $[ \, ] $ shows a greatest integer. This function is
- AA periodic function
- BA periodic function whose period is $\frac{1}{2}$
- ✓A periodic function whose period is $1$
- DNot a periodic function
✓
Answer
Correct option: C.
A periodic function whose period is $1$
c
(c) It is well known fact that fractional function always a periodic function whose period is $1.$
(c) 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$
$y = f(x),\,\,\,0, \le x + 3 < 1,\,\,\,0 \le x + 2 < 1$,
$0 \le x + 1 < 1$
$0 \le x < 1,\,\,1 \le x < 2$
$0 \le x < 1,\,\,0 \le x - 1 \le 1$.
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