Given that f (0) = 1, f ( n ) = 3 f ( n ? 1) if n is odd and n ? 1 and f ( n ) =

Question

Given that f(0) = 1, f(n) = 3f(n ? 1) if n is odd and n ? 1 and f(n) = 9f(n ? 2) if n is even and n ? 2 is a 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 the formula is valid.

a) Identify the formula for f(n)

Which one is correct

5. The definition is not valid

b) Identify the proof for the formula for f(n), obtained in part (a), using mathematical induction.

Which one is correct

Explanation / Answer

PartA=(2)

Part B= (1)

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