Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non-negative integers to the set of integers. If f is

well defined, find a formula for f(n) when n is a non-negative integer and prove that your formula is valid. a) f(0) = 0, f(n) = 2f(n – 2) for n >1 b) f(0) = 1, f(n) = f(n – 1) – 1 for n>=1 c) f(0) = 2, f(1) = 3, f(n) = f(n – 1) – 1 for n >= 2 d) f(0) = 1, f(1) = 2, f(n) = 2f(n – 2) for n>=2 e) f(0) = 1, f(n) = 3f(n – 1) if n is odd and n>=1 and f(n) = 9f(n – 2) if n is even and n>=2