Explanation : For f(x) = x - [x]; where [x] stands for the greatest integer ≤ x,
solving the equation f(x + T) = f(x),
we get T = 1 as the period.
f(x) = |cos(x)| is periodic with period π
n.f(x) = (x)cos(x) and
f(x) = sin(1/x)
if x ≠ 0; 0 otherwise are not periodic.