   Chapter 7.2, Problem 38ES ### 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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# Exercises 38 and 39 use the following definition: If f : R → R is a function and c is a nonzero real number, the function ( c ⋅ f ) ( x ) R → R is defined by the formula ( c ⋅ f ) ( x ) = c ⋅ ( f ( x ) ) for every real number x.Let f : R → R  be a function and c a nonzero real number. If f is one-to-one? Justify your answer.

To determine

To check:

If f: is a one-to-one function and c is a nonzero real number, then whether cf is also one-to-one function or not.

Explanation

Given information:

The function f: is a one-to-one function and c is a nonzero real number.

Function (cf): is defined by the formula (cf)(x)=cf(x) for all real numbers x.

Concept used:

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

Calculation:

It is given that f is one-to-one.

We have to check if cf is one-to-one or not.

By hypothesis, we have f(x)=f(y)x=y

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