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 greaterthanorequalto 1 b) f(0) = 1, f(1) = 0, f(2) = 2, f (n) = 2f (n - 3) for n greaterthanorequalto 3 c) f(0) = 0, f(1) = 1, f(n) = 2f (n + 1) for n greaterthanorequalto 2 d) f(0) = 0, f(1) = 1, f(n) = 2 f (n - 1) for n greaterthanorequalto 1 e) f(0) = 2, f(n) = f(n - 1) if n is odd and n greaterthanorequalto 1 and f(n) = 2f(n - 2) if n greaterthanorequalto 2