Let be defined by . Find a necessary and sufficient condition on and for . What is the largest interval I you can find on which g is injective? Find (ie. find the set {g(x): x I}).

Find an explicit formula for the inverse to

by the quadratic formula. The same applies for x_1.

Since . Hence the necessary and sufficient condition is .

Since this is a map from the reals to the reals, .

Can someone check those?

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