   Chapter 7.2, Problem 15ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In each of 15-18 a function f is defined on a set of real numbers. Determine whether or not one-to-one and justify answer. f ( x ) = x + 1 x , for each number x ≠ 0

To determine

To check:

Whether a given function f is one-to-one or not.

Explanation

Given information:

f(x)=x+1x, for all real numbers x0.

Concept used:

In one-to-one function, distinct elements in domain are mapped with distinct elements in codomain.

Calculation:

If f is a function defined on an infinite set X, then f is one to one if and only if the following universal statement is true.

x1,x2X,if f(x1)=f(x2) then x1=x2.

In this case, the function f(x)=x+1x defined on {0}.

Let x1,x2{0}

To determine one-to-one, consider f(x1)=f(x2)

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