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...