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

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
Correct answer is B. Homomorphism exists

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