Question 91
Define $f$ on the unit square $S = [0, 1] \times [0, 1] = \{(x, y) \in \mathbb{R}^2 : 0 \le x, y \le 1\}$ by
$$
f(x, y) = x\sqrt{1-y^2} + y\sqrt{1-x^2}.
$$
Prove that $f$ maps $S$ onto the unit interval $[0, 1]$. Is $f$ one-to-one on $S$?
$$
f(x, y) = x\sqrt{1-y^2} + y\sqrt{1-x^2}.
$$
Prove that $f$ maps $S$ onto the unit interval $[0, 1]$. Is $f$ one-to-one on $S$?