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Prove that the mapping given in Example 3 is a

Chapter 10, Problem 2E

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QUESTION:

Problem 2E

Prove that the mapping given in Example 3 is a homomorphism.

Reference:

EXAMPLE 3 The mapping f from R* to R*, defined by Φ (x) = |x|, is a homomorphism with Ker Φ = {1, 21}.

Questions & Answers

QUESTION:

Problem 2E

Prove that the mapping given in Example 3 is a homomorphism.

Reference:

EXAMPLE 3 The mapping f from R* to R*, defined by Φ (x) = |x|, is a homomorphism with Ker Φ = {1, 21}.

ANSWER:

Step 1 of 2

A group homomorphism  is a mapping that satisfies operation-preserving:

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