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# Show that if f and g are real-valued functions such that

ISBN: 9780073383095 37

## Solution for problem 39E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 39E

Show that if f and g are real-valued functions such that f(x) is O(g(x)), then for every positive integer n, fn(x) is O(gn(x)). [Note that fn(x) = f(x)n.]

Step-by-Step Solution:
Step 2 of 3

Step1:

In this problem, we have to prove that for every positive integer n, fn(x) is O(gn(x))  [Note that fn(x) = f(x)n.]

Step 2:

Let us consider if f and g are real-valued functions such that f(x) is O(g(x))

We can say that f(x) is O(g(x)) if there are constant C and k such that |f(x)||g(x)| whenever x>k

Similarly for this case f(x) is O(g(x)) there are constant C and 1

such that |f(x)|

Step 3 of 3

##### ISBN: 9780073383095

The full step-by-step solution to problem: 39E 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: 7. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: every, functions, Integer, Note, Positive. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Show that if f and g are real-valued functions such that f(x) is O(g(x)), then for every positive integer n, fn(x) is O(gn(x)). [Note that fn(x) = f(x)n.]” is broken down into a number of easy to follow steps, and 28 words. Since the solution to 39E from 3.2 chapter was answered, more than 261 students have viewed the full step-by-step answer.

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