I have the function $$f(x,y)=(x+y,xy)\quad U=[{(x,y)\in \mathbb{R^2} |\quad 0 <y<x}] $$
I am trying to show that $f$ is global invertebility in $U$.
to do that I though on showing that $f$ is injective function in $U$ but I am not sure how to do that with the inequality I given in the set $U$