F(x_1,x_2,x_3) = (y_1,y_2,y_3) Set
(1) x_1/ (x_1 + x_2 + x_3) = y_1
(2) x_2/ (x_1 + x_2 + x_3) = y_2
(3) x_3/ (x_1 + x_2 + x_3) = y_3
1. Prove that F is injective.
2. Without appealing to the Inverse Function Theorem, find the investment directly.
3. Find the domain of F
4. Find the range of F, which is the domain of F^-1.
5. Explain why J_f(x) 6=0 when x € Dom (F)
