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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 52E

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Question

Find the kernels and images of the following homomorphisms. Which of the homomorphisms are
injective? Which are surjective?
(i) The mapping 0 : Z₁₁ → Z₁₁ given by 0(x) = x².
(ii) The mapping : R* → R* given by p(x) = x³.
(iii) The mapping & : G → G given by y(x) = g¯-¹xg for x = G where G is a group and g € G.
(You may assume that this is a homomorphism.)

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