Determine whether each of these proposed definitions is a

Chapter 5, Problem 5E

(choose chapter or problem)

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) = 2 f (n ? 2) for n ? 1________________b) f (0) = 1, f( 1) = f (n ? 1) ? 1 for n ?1________________c) f (0) = 2, f (1) = 3, f (n) = f(n ? 1) ? 1 for n ? 2________________d) f (0)= 1. f (1) = 2, f (n) = 2 f (n ? 2) for n ?2________________e) f (0) = 1, f(n) = 3 f (n ?1) if n is odd and n ?1 and f(n) = 9 f(n ? 2) if n is even and n ?2

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