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Let $f(x,y)=(\frac{1}{2} x^2 + x(y-1)^3, xy-x)$
(1) Find a formula for $f^{-1}$ in a small ball $B(b,r)$ where $b=(\frac{1}{2}, 0)$.
(2) Give an example of a radius $r>0$ for which the inverse function is well defined.


I showed that the inverse was well defined in some neighbourhood of b in a previous question using the Inverse Function Theorem.

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    Sorry, I may be missing something, but how can you invert a function of two variables? Your function is from $R^2$ to $R$, so it cannot be a simple function, so it can't be (fully) inverted. The inverse function would have to be from $R$ to $R^2$, right?2011-06-09
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    @Lubos: The function is from $R^2$ to $R^2$.2011-06-09
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    I see, thanks, it's a comma. ;-)2011-06-09

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