   Chapter 7.2, Problem 39ES ### 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 onto, is c ⋅ f also onto? Justify your answer.

To determine

To check:

If f: is an onto function and c is a nonzero real number, then whether cf is also onto function or not.

Explanation

Given information:

The function f: is onto 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:

A function h: is said to be onto if, for every y, there exists x such that h(x)=y.

Calculation:

Consider r. Since the function f is onto from  to , there exists a real number x such that

f(x)=rc

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