6. 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) 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