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.

Please explain why the following are not valid defintions.

Part A: f (0) = 0, f (1) = 1, f (n) = 2f (n + 1) for n 2

Part B: f (0) = 0, f (1) = 1, f (n) = 2f (n 1) for n 1