I would do this in a slightly different way: gives ; so or so either or . Since or , the equation is not satisfied, we must have .
That's a quadratic equation in y: so by the quadratic formula, . It is that " " that means it does NOT have, strictly speaking, an inverse.The inverse is a bit harder to find.
and from here all the ways i've tried have lead to y's on both sides of the equation. If you substitute into g(x) you end up with the same function (in terms of k). I haven't been able to use this to my advantage though