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Mathematics, 16.04.2020 00:28 cairolove228
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 β 2) for n β₯ 1
b) f (0) = 1, f (n) = f (n β 1) β 1 for n β₯ 1
c) f (0) = 2, f (1) = 3, f (n) = f (n β 1) β 1 for n β₯ 2
d) f (0) = 1, f (1) = 2, f (n) = 2f (n β 2) for n β₯ 2
e) f (0) = 1, f (n) = 3f (n β 1) if n is odd and n β₯ 1 and f (n) = 9f (n β 2) if n is even and n β₯ 2.
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