First, sorry for the incorrect terminology, I'm not sure what else to call this.

I know it is possible to use the group to show that a function f(x) breaks down into the sum of an even and an odd function. Since I can't find my notes or reference on the subject my questions are

1) How do you do this using

and

2) How do you generalize this process? As an example, how can you do this with, say, ?

Thanks!

-Dan