1. The problem statement, all variables and given/known data A function f:R-->R^x is a homomorphism iff f(x+y) = f(x) + f(y) for all x,y in R 2. Relevant equations I dont know what group R^x is. I can only assume it means Reals under multiplication . Would that mean that f(x+y) = f(x)f(y)? How does the function work? Since 5 is in R what would it be mapped to in t R^x? 3. The attempt at a solution This isnt a homework question, I read it in the book as a false statement but there was no explaination as to what R^x was and I couldnt understand why it was false.