What do you mean by "elements"?I can't as long as I don't know where your elements are taken from.
##f(x),g(x),C##What do you mean by "elements"?
This is what I meant.##f(x),g(x),C##
If they were, as usual, from ##\mathbb{R}##, then the answer would be: because ##(\mathbb{R},+)## is a group. But if you had defined addition differently on some set, then there is not enough information about it.
Being in a group means existence of an additive inverse, -C.I just looked over the wikipedia page for groups and now understand why ##(\mathbb{R},+)## is a group, but why does belonging to a group imply reversibility?
##x \longmapsto e^x## or ##x \longmapsto x^n## e.g. by the theorem of invertible functions or in general step by step. They aren't operations anymore, just other functions.How would we prove the reversibility of other operations such as exponentiation (for values >= 0), that don't belong to groups?