Let E= {P, P2, PN} be a finite subset of a closed interval [a, b], and...

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Let E= {P₁, 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(P₁)Xpi (x) + 9(P₂)X₂ (x) + + g(PN)XpN (T); Let E= {P₁, 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(P₁)Xpi (x) + 9(P₂)X₂ (x) + + g(PN)XpN (T);