Question

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 exists

I 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 1

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)=2*a is a homomorphism because f(a+b)=2a+b = 2a*2b = f(a)*f(b). Again f is also one-to-one and onto T and T’ are isomorphic.