Is the function (f(x) =x-[x] periodic? If so, what is the period?

Answer 1

As is often the case I want to make certain the problem has been correctly entered. This is the function "X minus the greatest integer of X."

Take any x, find f(x), find f(x+1) too. You will discover f(x) = f(x+1). Yes, it is periodic with a period of 1.