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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