   Chapter 7.2, Problem 37ES ### 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
1 views

# Exercise 36 and 37 use the following definition: If f : R → R and g : R → R are functions, then the function ( f + g ) : R → R is defined by the formula ( f + g ) ( x ) = f ( x ) + g ( x ) for every real number x.If f : R → R and g : R → R are both onto, is f + g also onto? Justify your answer.

To determine

To check:

If f: andg: are both onto functions, then whether f+g is onto function or not.

Explanation

Given information:

The functions f: andg: are both onto functions.

Concept used:

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

Calculation:

Consider that f: and g: be two onto functions.

Objective is to determine that (f+g): is onto or not.

Claim: The function (f+g): is not necessarily onto.

For this consider, the function f: and g: defined by,

f(x)=x and g(x)=x

Then, clearly these two functions are onto

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