1. Let F(-oo, co) = {f : R - R} be the set of all functions from the real numbers to the real numbers, as in the book. (a) Let Qn be the subset of F(-co, co) consisting of all functions which are polynomials of degree exactly n for n 2 0. Show that this is not a subspace. (b) Let Pn be the subset of F(-co, co) consisting of all functions which are polynomials of degree at most n > 0. Show that this is a sub- space. (c) Describe the set of all polynomials f(I) = do + alIt .. . + 03.1. in Pa with the property f(1) =1, by forming equations on the coef- ficients, and finding the general solution. Is this a subspace of Pa? (d) Let U = {f(x) E P3 : f(1) =0, f'(1) =0} be the subspace of those polynomials whose value and first derivative at r = 1 are zero. De- scribe U as the span of some polynomials in P3