Let E= {P, P2, PN} be a finite subset of a closed interval [a, b], and g: [a, b] R be a function such that g(x) = 0 for all z [a, b]\ E. (a) Using the function Xp(r) defined in Problem 2, show that one can express the function g as g(x) = g(P)Xpi (x) + 9(P)X (x) + + g(PN)XpN (T);