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Australian National UniversityMATH 1005Math_Tutorial_Review 63

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NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine whether each of these proposed definitions is a valid recursive definition of a function f from the ...

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 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. Section Break Difficulty: Easy f(0) = 0, f(n) = 2f(n – 2) for n ≥ 1 Choose the correct statement. (You must provide an answer before moving to the next part.) The definition of f is not valid because f(n) must be defined in terms of f(n – 1), not in terms of f(n – 2). The definition of f is not valid because defining f(1) would require f(–1), which is not available. The definition of f is valid. The definition of f is not valid because defining f(1) would require f(–1), which is not available. The definition of f is not valid because defining f(1) would require f(–1), which is not available. Hint #1 f(0) = 1, f(n) = f(n – 1) – 1 for n ≥ 1 Choose the correct statement. (You must provide an answer before moving to the next part.) The definition of f is not valid because f(n) decreases as n increases. The definition of f is valid. The definition of f is not valid because defining f(1) would require f(–1), which is not available. The given statement is valid. We can solve f(1) using the given initial conditions. The definition of f is valid. Hint #1     References     References References Hints Hints64. Award: 1.00 point Problems? Adjust credit for all students. Required information Given the function f(n) defined as f(0) = 1, f(n) = f(n – 1) – 1 for n ≥ 1. Choose the correct formula for f(n) when n is a nonnegative integer. (You must provide an answer before moving to the next part.) f (n) = 1 + n f (n) = n – 1 f (n) = 1 – n f (n) = 2n + 1 The correct formula for f(n) when n is a nonnegative integer is f(n) = 1 – n. f (n) = 1 – n

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