to show it is a homomorphism you must show that for all

can you show this? try it and tell us what you get.

the kernel of , , is the set of all such that . (why 1? because it is the identity element with respect to multiplication on the reals). So, what numbers are in this set?

Here is what an isomorphism is: in a nutshell, it is a homomorphism that is one-to-one and onto.

so, is one-to-one and onto?