Problem 2 Consider the interval [-1, 1] = {r e R : -1 f =0 (where f = 0 means f(x) = 0 for all x e [-1, 1]). (b) Let fe C([-1, 1]) be given by f(x) = 3r + 1. Find the condition on a, be R such that ge C([-1, 1]) given by g(x) = ar + b satisfies fog = 0. (c) Find a formula for a function T: R2 - C([-1, 1]) that satisfies T([a, b]) OT([c, d]) = [a, b] . [c, d) for all [a, b], [c, d] ER?. Note that the . on the right of the equation is just the usual dot product of vectors in R?. Make sure you explain your thought process that led you to arrive at your answer, and show why your formula works