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)if n is odd and n ≥ 1 and f (n) = 2f (n − 2) if n ≥ 2