Solved: Determine whether each of these functions is a

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

ISBN: 9780073383095 37

Solution for problem 23E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 23E

Determine whether each of these functions is a bijection from R to R

Step-by-Step Solution:

Step 1 :

We have to check weather the following function are bijection from $R\ to\ R$ .

given functions are

(a) $f(x)=2x+1$

Ans :

First check the given function is one-one

$\forall{}a,b\epsilon{}R\ \ \ \ f(a)=f(b)$

Such that $a=b$

.’. The given function is one-one.

next we to check the onto

In the given function the range is real numbers $2((y-1)/2)+1=y.$

.’. The function is onto

Hence the function $f(x)=2x+1$ is bijective.

Step 2 :

(b) $f(x)={x}^{2}+1$

Ans :First check the given function is one-one

consider $f(2)={2}^{2}+1=(-2{)}^{2}+1=5$

we can have the same values of $f(x)$ even the different values of x,

.’. the function is not one one

Hence the function $f(x)={x}^{2}+1$ is not bijective.

Step 3 of 4

Chapter 2.3, Problem 23E is Solved

Step 4 of 4

Textbook: Discrete Mathematics and Its Applications

Edition: 7

Author: Kenneth Rosen

ISBN: 9780073383095

The full step-by-step solution to problem: 23E from chapter: 2.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “Determine whether each of these functions is a bijection from R to R” is broken down into a number of easy to follow steps, and 13 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 23E from 2.3 chapter was answered, more than 245 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: bijection, determine, functions, these, whether. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.