Show that R^x/<-1> is isomorphic to the group of positive real numbers under multiplication.
I know I need to show we have a homomorphism, and is one - to one and onto in order to be isomorphic. I know all that, but I don't know what function mapping to use.
That is not the standard first isomorphism theorem for groups, which you can read in one of the following sites:
Isomorphism theorem - Wikipedia, the free encyclopedia
http://www.tjsullivan.org.uk/math/morphthm.pdf (pages 5-6)
http://marauder.millersville.edu/~bi...o/firstiso.pdf
If you look at the above carefully then you'll understand why the absolute value function solves your problem.
Tonio