Let f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)). Prove or disprove the following statement:
Let f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)). Prove or disprove the following statement:
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Let f (n) and g(n) be positive functions (for any n they give positive values) and f (n) = O(g(n)).
Prove or disprove the following statement:
![2.f(n) = 0(28(n))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F474a784e-9f95-4813-81d7-a60d3fc34f86%2Fab46b078-17b5-4a34-a34b-1da1a16e7526%2F3x5l5w8_processed.png&w=3840&q=75)
Transcribed Image Text:2.f(n) = 0(28(n))
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Is this answer correct? It seems as if you mention that 2^(f(n)) is always an upper bound for 2^(c*g(n)), which is not right consider the statement (should be the other way around). Also, how does this statement, "Since 2 f(n) is an exponential function with a positive base, it grows much faster than any polynomial function g(n)." give us any inference on the upper bound?
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