A function defined by f(x)=2*x such that f(x+y)=2x+y under the group of real numbers, then ________(a) Isomorphism exists(b) Homomorphism exists(c) Heteromorphic exists(d) Association existsI had been asked this question by my college director while I was bunking the class.The above asked question is from Group Axioms topic in chapter Groups of Discrete Mathematics

A function defined by f(x)=2*x such that f(x+y)=2x+y under the group o

1.	A function defined by f(x)=2*x such that f(x+y)=2x+y under the group of real numbers, then ________(a) Isomorphism exists(b) Homomorphism exists(c) Heteromorphic exists(d) Association existsI had been asked this question by my college director while I was bunking the class.The above asked question is from Group Axioms topic in chapter Groups of Discrete Mathematics
Answer» Correct answer is (b) Homomorphism exists The best EXPLANATION: Let T be the group of real numbers under ADDITION, and let T’ be the group of positive real numbers under multiplication. The mapping F: T -> T’ deﬁned by f(a)=2a is a homomorphism because f(a+b)=2a+b = 2a2b = f(a)*f(b). Again f is also one-to-one and onto T and T’ are isomorphic.

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