Determine whether each of these functions from Z to Z is

Chapter 1, Problem 12E

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QUESTION:

Determine whether each of these functions from Z to Z is one-to-one.

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QUESTION:

Determine whether each of these functions from Z to Z is one-to-one.

ANSWER:

Answer:Step-1: In this problem we need to determine whether each of the given functions from Z to Z is one-to -one (or) not. One -to-one function: A function for which every element of the range of the function corresponds to exactly one element of the domain. Test for one -to-one functions : If f(a) = f(b) implies that a = b , then f is one-to-one.1. In this problem we need to determine f(n) = n-1 is one -to-one (or) not. Let us consider , , where . Now , test for one-to-one functions: Assume that , f(n) = f(p) , since given f(n) = n-1 . Therefore , f is one -to-on

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