Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid. a) f(0) = 1, f(n) =−f(n−1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n−3) for n ≥ 3 c) f(0) = 0, f(1) = 1, f(n) = 2f(n+1) for n ≥ 2 d) f(0) = 0, f(1) = 1, f(n) = 2f(n−1) for n ≥ 1 e) f(0) = 2,f(n) = f(n−1)ifnisoddandn ≥ 1and f(n) = 2f(n−2) if n ≥ 2