Explanation Given information: f and g are real-valued functions defined on same non-negative integers and f ( n ) ≥ 0 , g ( n ) ≥ 0 for all n ≥ r and r is any real number greater than zero. Formula used: Let f and g be real valued functions defined on the same nonnegative integers, with g ( n ) ≥ 0 for every integer n ≥ r , where r is positive real number. Then, f is of order g , written f ( n ) is Θ ( g ( n ) ) , if and only if, there exist positive real numbers A , B and k ≥ r such that A g ( n ) ≤ f ( n ) ≤ B g ( n ) for every integer n ≥ k . Proof: If f ( n ) is Θ g ( n ) , according to the definition of the Θ notation, there exist A , B and k positive real numbers with

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 11.2, Problem 18ES

To determine

To prove:

If f(n) is Θg(n), then g(n) is Θf(n) when f and g are real-valued functions defined on the same non-negative integers.

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Chapter 11.2, Problem 17ES

Chapter 11.2, Problem 19ES

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To prove: If f ( n ) is Θ g ( n ) , then g ( n ) is Θ f ( n ) when f and g are real-valued functions defined on the same non-negative integers.

Solution Summary: The author explains how f(n)isTheta g (r) are real-valued functions defined on the same non-negative integers.

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To prove:

If f(n) is Θg(n), then g(n) is Θf(n) when f and g are real-valued functions defined on the same non-negative integers.

Want to see the full answer?

Chapter 11 Solutions

To prove: If f ( n ) is Θ g ( n ) , then g ( n ) is Θ f ( n ) when f and g are real-valued functions defined on the same non-negative integers.

Solution Summary: The author explains how f(n)isTheta g (r) are real-valued functions defined on the same non-negative integers.

Concept explainers

Videos

To prove: If f(n) is Θg(n), then g(n) is Θf(n) when f and g are real-valued functions defined on the same non-negative integers.

Want to see the full answer?

Chapter 11 Solutions

To prove:

If f(n) is Θg(n), then g(n) is Θf(n) when f and g are real-valued functions defined on the same non-negative integers.