Suppose g is a continuous function on [0, 1]. For f in C([0, 1]) define Tf by (If) (x) = g(x) +> / ex-tf(t) dt. a. Find a range of values of A for which T is a contraction with respect to the supremum norm on C( [0, 1]). b. Find a range of values of A for which T is a contraction with respect to the L2-norm on C([0, 1]). c. Describe the iterative process for finding a solution f to the equation f(x) = g(2) + > ex-tf(t) dt explaining how the procedure works and how one knows that it leads to a solution. d. With fo(x) = 0 for all x, compute the first three iterates, f1, f2, and f3