# Solved: Show that if f(x) and g(x) are functions from the ## Problem 33E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 33E

Show that if f(x) and g(x) are functions from the set of real numbers to the set of real numbers, then f(x) is ? (g (x)) if and only if there are positive constants k, C1, and C2 such that C1|g(x)| ? |f(x)| ? C2|g(x)| whenever x > k.

Step-by-Step Solution:

Solution Step 1:f(x) and are the functions from set of real numbers to the set of real numbers,then we have to prove is if and only if there are positive constants k,and such that .Step 2:First we will prove is implies there are positive constants k,and such that and there are positive constants k,and such that implies is Consider is then there are some constants and such that for all …(1)And for all for all (multiply both sides by ..(2)From (1) and (2) we get …(3)Thus we proved is implies there are positive constants k,and such that …(4)

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Step 4 of 4

##### ISBN: 9780073383095

Since the solution to 33E from 3.2 chapter was answered, more than 238 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 33E from chapter: 3.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. The answer to “Show that if f(x) and g(x) are functions from the set of real numbers to the set of real numbers, then f(x) is ? (g (x)) if and only if there are positive constants k, C1, and C2 such that C1|g(x)| ? |f(x)| ? C2|g(x)| whenever x > k.” is broken down into a number of easy to follow steps, and 49 words. This full solution covers the following key subjects: real, set, Numbers, constants, Positive. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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