1. The problem statement, all variables and given/known data Let f= (f_1, f_2, f_3) be a vector valued function defined (for every point (x_1,x_2,x_3) in R^3 for which x_1 + x_2 + x_3 is not equal to -1) as follows: f_k (x_1,x_2,x_3) = x_k /( 1+x_1+x_2+x_3) where k =1,2,3. After some computations I found that the determinant of the Jacobian matrix is (1+x_1+x_2+x_3)^(-4) (which coincides with the answer of the book). Then, by the inverse function theorem, it follows that f is one to one since the determinant is nonzero. The problem is the following: Compute f^(-1) explicitly. How can I do this???? http://en.wikipedia.org/wiki/Inverse_function_theorem Gives a formula to find the inverse of the jacobian matrix, but I'm trying to find the inverse of the function. How to do this? 3. The attempt at a solution I don't see how to find the inverse explicitly, I know it exists because the determinant of the Jacobian is nonzero everywhere.