Is the Inverse of F(x) = x/(1+x+y+z) Possible to Find?

[Dave 72]

trying to find the inverse of z=x/(1+x+y+w)

 

[quantumdude]

What are your thoughts on the matter?

 

[Dave 72]

this is the function I'm actually dealing with:

F=<f_1, f_2, f_3> , where f_k(x_1,x_2,x_3) = x_k/(1+x_1+x_2+x_3) for k=1,2,3 and where x_1+x_2+x_3 is not -1 for all x_1,x_2,x_3

using the inverse function theorem, i found the jacobian to be (1+x_1+x_2+x_3)^(-4) which is not zero, and since all the 1st order partial derivatives exist and are continuous, this makes me think that F has an inverse, but actually finding out what it is is where I'm getting stuck