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, ind a formula for f(n) when n is a nonnegative integer and prove that your formula is valid. a) f(0) l, f(n)--f(n-1) for n > 1 b) f(0)= I. f(!)=0. f(2)=2. f(n)=2f(n-3) for n > 3 f(0)-2. f(n) f (n) 2f (n - 2) if nz 2 e) f(n-l ) f n is odd and n > 1 and