inverse of sum of functions

[jburto2]

I have been working on a problem in my generalized linear models class, and I have a simple question about inverse functions.

Without going into detail of the problem, is it possible to take an inverse of a sum of functions?
For instance, say f(x)+f(x/a) = g(mu)

Can I conclude that x + x/a = f[sup:2pvoddm3]-1[/sup:2pvoddm3][g(mu)] ?

Thanks

 

[daon]

For linear functions that would work, since

f(x)+f(x/a) = f(x+x/a).

For general non-linear functions it would not.

 

[jburto2]

So this would not work for a sum of standard normal cumulative distribution functions?

 

[daon]

The bell curve is:

\(\displaystyle f(x)=ae^{-bx^2}\)

Try yourself to see if f(x)+f(y)=f(x+y).

edit: Sorry I misread your post above, and I did not see "cumulative". Someone more familiar with that function will have to help you.