In the following, f(x), g(x) and h(x) are all positive value real functions. (Note: Answer true if for any possible positive value real function f(x) g(x) and h(x), the statement is true. If a counter example of f, g, and h can make the statement false, then it is false.) If f(x) is O(g(x)), then 2f(x) belongs to O(g(x)) If f(x) is O(g(x)), g(x) is O(h(x)), then f(x) belongs to O(h(x)) If f(x) and g(x) are O(n^2), then f(x)+g(x) belongs to O(n^2)

In the following, f(x), g(x) and h(x) are all positive value real functions. (Note: Answer true if for any possible positive value real function f(x) g(x) and h(x), the statement is true. If a counter example of f, g, and h can make the statement false, then it is false.) If f(x) is O(g(x)), then 2f(x) belongs to O(g(x)) If f(x) is O(g(x)), g(x) is O(h(x)), then f(x) belongs to O(h(x)) If f(x) and g(x) are O(n^2), then f(x)+g(x) belongs to O(n^2)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter16: Probabilistic Inventory Models

Section16.3: The News Vendor Problem: Discrete Demand

Problem 9P

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Question

In the following, f(x), g(x) and h(x) are all positive value real functions.
(Note: Answer true if for any possible positive value real function f(x) g(x) and h(x), the statement is true. If a
counter example of f, g, and h can make the statement false, then it is false.)
If f(x) is O(g(x)), then 2f(x) belongs to O(g(x))
If f(x) is O(g(x)), g(x) is O(h(x)), then f(x) belongs to O(h(x))
If f(x) and g(x) are O(n^2), then f(x)+g(x) belongs to O(n^2)
If f(x) and g(x) are O(n^2), then f(x)-g(x) belongs to O(n^2)
If f(x) is O(g(x)), and g(x) is O(n), then f(x)+g(x) belongs to O(n)
If f(x)/g(x) = 100 for all x > 1000, then f(x) belongs to O(g(x))
%3D
If f(x) belongs to O(g(x)), then 2^f(x) belongs to O(2^g(x))

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