I have been working on a project where I have a function F(x) which is closely related to a function G(x). The function G(x) has been well studied already and tools exist for using it. To make the equations I derive for F(x) useful I wanted to convert them into G(x) so that people can evaluate things for F(x) using the tools that already exist for G(x)

So far I derived their relationship

So for example if I had this equation to find an important number B

I could turn it into

And use the tools that exist for G(x) to find B for any y

But I am stuck when it comes to their inverse functions. As an example of this I have derived the equation

I am confused about how I can use the relationship to get L in terms of the inverse function of . I am not even sure if this is possible to do