A Book of Abstract Algebra

Charles C. Pinter

Chapter 6

FUNCTIONS - all with Video Answers

Educators

Section 1

A

Problem 1

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=3 x+4$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 2

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=x^{3}+1$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 3

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=|x|$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 4

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=x^{3}-3 x$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 5

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=\left\{\begin{array}{c}x \text { if } x \text { is rational } \\ 2 x \text { if } x \text { is irrational }\end{array}\right.$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 6

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
$f(x)=\left\{\begin{array}{l}2 x \text { if } x \text { is an integer } \\ x \text { otherwise }\end{array}\right.$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 7

Proof By exhibiting a counterexample: $-1$ is not equal to $f(x)$ for any $x \in \mathbb{R}$.
Determine the range of each of the functions in parts 1 to $6 .$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator