b) Consider the function f(x) = = x - 2k x + k 2k , k = 1, 2, 3, and π, where is the floor function. b.1) Show that f is 2k- periodic function and f (x) = x for all x = (−k, k). b.2) For k 1, consider the function g (x) = f² (x) = (x· = x- 2k[]). b.2.1) Show that 9 is periodic with period 2. [Hint: use b.1 and above a)] b.2.2) Show that g (x) = x², for −1 < x < 1. b3) Assume that f (x) is the restriction of a 2k- periodic function g (x) to the interval (—k, k). Show that the 2p- periodic 9 (x) function can be described by the function g (f (x)) for all x Є R.