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

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 24E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 24E

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

Step-by-Step Solution:

Step 1:

In this problem we have to show that f(x) is strictly increasing if and only if the function g(x) = 1/f(x) is strictly decreasing .

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.

Step 3 of 4

Chapter 2.3, Problem 24E is Solved
Step 4 of 4

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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