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# Let f: R R and let f(x) > 0 for all .x R. Show f(x) is

ISBN: 9780073383095 37

## Solution for problem 25E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 25E

Let f: R ? R and let f(x) > 0 for all .x ? R. Show f(x) is strictly decreasing if and only if the function g(x) = 1/f(x) is strictly increasing.

Step-by-Step Solution:

Solution :Step 1: In this problem we have to show that f(x) is strictly decreasing if and only if the function g(x) = 1/f(x) is strictly increasing . Step 2: definition of strictly increasing and strictly decreasing .Strictly Increasing : A function is called strictly increasing , if for all x and y such that x < y then it has f(x) < f(y) . this is also called strictly monotonic increasing function.Strictly Decreasing : A function is called strictly decreasing , if for all x and y such that x > y then it has f(x) > f(y) . this is also called strictly monotonic decreasing function.

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##### ISBN: 9780073383095

The answer to “Let f: R ? R and let f(x) > 0 for all .x ? R. Show f(x) is strictly decreasing if and only if the function g(x) = 1/f(x) is strictly increasing.” is broken down into a number of easy to follow steps, and 32 words. This full solution covers the following key subjects: strictly, let, increasing, function, show. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 25E from 2.3 chapter was answered, more than 289 students have viewed the full step-by-step answer. 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. The full step-by-step solution to problem: 25E from chapter: 2.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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