Answered: Define H : Z → Z by the rule H(x) = 4x…

Define H : Z → Z by the rule H(x) = 4x – 5, for all integers x. (Z: set of integers) (a) Is H one-to-one? Prove or give a counterexample. (b) Is H onto? Prove or give a counterexample.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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Define H : Z → Z by the rule H(x) = 4x – 5, for all integers x. (Z: set of integers)
(a) Is H one-to-one? Prove or give a counterexample.
(b) Is H onto? Prove or give a counterexample.

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