(a) Let R* be the multiplicative group of nonzero real numbers, R** be the multiplicative group of positive real numbers and ƒ : R* →→ R** be defined by f(x)=x². (i) Check as to whether f is a homomorphism or not [Hint: first check as to whether f is well defined or not] (ii) If f is a homomorphism, then find its kernel
(a) Let R* be the multiplicative group of nonzero real numbers, R** be the multiplicative group of positive real numbers and ƒ : R* →→ R** be defined by f(x)=x². (i) Check as to whether f is a homomorphism or not [Hint: first check as to whether f is well defined or not] (ii) If f is a homomorphism, then find its kernel
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![(a) Let R* be the multiplicative group of nonzero real numbers, R** be the multiplicative group of
positive real numbers and ƒ : R* →→→ R** be defined by f(x) = x².
(i) Check as to whether f is a homomorphism or not
[Hint: first check as to whether f is well defined or not]
(ii) If f is a homomorphism, then find its kernel](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabdd1821-d7b6-4171-a67e-edf70418727b%2F6755f45e-e6f1-49b0-b5b7-4233708f7af9%2Follxn8f_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let R* be the multiplicative group of nonzero real numbers, R** be the multiplicative group of
positive real numbers and ƒ : R* →→→ R** be defined by f(x) = x².
(i) Check as to whether f is a homomorphism or not
[Hint: first check as to whether f is well defined or not]
(ii) If f is a homomorphism, then find its kernel
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