Originally Posted by

**Mathnasium** To verify that two functions, f(x) and g(x) are inverses, is it absolutely necessary to do BOTH f(g(x)) and g(f(x)) and show that they are both equal to x?

I was pretty sure I was taught that it was necessary to do both, but I've never seen one of the two compositions work out to equal x and the other work out to be something else.

If it IS necessary to do both, can someone provide an f(x) and g(x) where the composition equals x in one "direction" and something else in the other?

Just curious.