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Question-1 Is it true: for any given $C^1$ continuous real function $f(x, y): \Re^2 \to \Re^1$, there exist $C^1$ continuous real functions $\Psi(x), w(x,y), u(x)$ such that: $u(f(x,y))=u(x)\Psi(\frac{w(x, y)}{u(x)})$ where $\frac{du(x)}{dx}\Ge \frac{du(x)}{dx}\ge 0$; $\frac{\partial w(x, y)}{\partial y}\Ge y}\ge 0$
Question-2 Can these functions $\Psi(x), w(x,y), u(x)$ be solved, analytically or approximately?