Detennine whether each of these proposed definitions is a
Chapter 4, Problem 4.3.5(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) = 0, fen) = 2f(n - 2) for n 1 b) f(O) = 1, fen) = fen - 1) - 1 for n 1 c) f(O) = 2, 1(1) = 3, f(n) = fen - 1) - l for n 2 d) f(O) = 1, f(I) = 2, fen) = 2f(n - 2) for n 2 e) f(O) = I, f(n) = 3f(n - l) ifn is odd and n l and f(n) = 9 fen - 2) if n is even and n 2
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