# In 10—14 S denotes the set of real numbers strictly between 0 and 1. That is, S = { x ∈ R | 0 &lt; x &lt; 1 } . * 14. Define a function g from the set of real numbers to S by the following formula: For each real number x , g ( x ) = 1 2 ⋅ ( x 1 + | x | ) + 1 2 . Prove that g is a one-to-one correspondence. (It is possible to prove this statement either with calculus or without it.) What conclusion can you draw from this fact?

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section
Chapter 7.4, Problem 14ES
Textbook Problem

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