   Chapter 7.2, Problem 36ES ### 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 one-to-one, is f + g also one-to-one? Justify your answer.

To determine

To check:

If f: and g: are both one-to-one, then whether f+g is one-to-one or not.

Explanation

Given information:

f:  and g:  are one-to-one functions.

Concept used:

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

Calculation:

Let f: define f(x)=x and g:

define

f(x)=x.

Now to show that the functions f and g are both one-to-one.

Let x1,x2 implies f(x1),f(x2).

Consider,

f(x1)=f(x2)x1=x2      Since f(x)=x.

By the definition of one-to-one function, f is one-to-one.

Let x1,x2 implies g(x1),g(x2).

Consider

g(x1)=g(x2)x1=x2    Since g(x)=x

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