Suppose we have a polynomial f(x) = x* + ck-1xk-1+ ...+ c2x2 + cix + co.(a) Can we determine f (x) with k points? If so, provide a set of inputs x0,x1, . . . ,xk_1 such that knowing points (x0, f (xo)), (x1, f (x1)), . . . , (xk_1, f (xk_1)) allows us to uniquely deter- mine f (x), and show how f (x) can be determined from such points. If not, provide a proof of why this is not possible. (b) Now, assume each coefcient is an integer satisfying 0 g c;-