I just got through a lession @ purple math about functions.
The last example, in the proving that two functions are inverses of each other gives a specific example where F(g(X)) would equal lxl, except that a domain restriction forces the answer to be greater or equal to zero, so the absolute value can be removed.
so, F(G(X))=x, and G(F(X))=lxl and are therefore not inverses of each other.
My question is, what if the domain restriction forcing F(G(X)) to be greater than or equal to 0, had not existed? You would end up solving for lxl for both compositions. They would still not be inverses of each other right?