Detennine whether each of these proposed definitions is a

Chapter 4, Problem 4.3.6

(choose chapter or problem)

Detennine 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 fonnula for f(n) when n is a nonnegative integer and prove that your fonnula is valid. a) f(O) = I, f(n) = -fen - 1) for n 1 b) f(O) = 1, f(l) = 0, f(2) = 2, fen) = 2f(n - 3) for n 3 c) f(O) = 0, f(I) = 1, fen) = 2f(n + 1) for n 2 d) f(O) = 0, f(I) = 1, fen) = 2f(n - 1) for n 1 e) f(O) = 2, f(n) = fen - 1) ifn is odd and n 1 and fen) = 2f(n - 2) if n 2