Hi, I really need help with this problem.

Thank you.

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) = 0, f(n) = 2f(n 2) for n 1

Choose the correct statement.

1). The definition of f is valid.

2). The definition of f is not valid because defining f(1) would require f(1), which is not available.

3). The definition of f is not valid because f(n) must be defined in terms of f(n 1), not in terms of f(n 2).