I don't think there is an upper or lower bound for that function. On the critical curve $x=1/(1-y)$, the function goes to negative infinity, and as, say, $y\to 1/2$ and $x\to 2$, the function goes to positive infinity.

I don't think there is an upper or lower bound for that function. On the critical curve $x=1/(1-y)$, the function goes to negative infinity, and as, say, $y\to 1/2$ and $x\to 2$, the function goes to positive infinity.