If x ∈ R, we define [[x]] to be the greatest integer n ∈ Z such that n < x. (Thus, for example, [[8:3]] = 8; [[π]] = 3; [[- π]] = -4.) The function x → [[x]] is called the greatest integer function. Determine the points of continuity of the following functions:
(a) f(x) := [[x]],
(b) g(x) := x [[x]],
(c) h(x) := [[sin x]].
(d) k(x) := [[1/x]] (x ≠ 0).