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Determine whether each of these proposed definitions is a valid recursive definition of a function f...

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Advance Math

Determine whether each of these proposed definitions is a validrecursive definition of a function f from the set of nonnegativeintegers to the set of integers. If f is well defined, find aformula for f(n) when n is a nonnegative integer and prove thatyour formula is valid.

a) f(0) = 1, f(n) = -f(n-1) for n ? 1

b) f(0) = 1, f(1) = 0, f(2) = 2, (n) = f(n-3) for n ? 3.

c) f(0) = 0, f(1) = 1, f(n) = 2 f(n + 1) for n ? 2

d) f(0) = 0, f(1) = 1, f(n) = 2 f(n - 1) for n ? 1

e) f(0) = 2, f(n) = f(n – 1) if n is odd and n ? 1 and f(n) =2f(n-2) if n ? 2.

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