(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Well I'm looking for a 'general' way about doing these problems. For example finding B = f(A) where f(x,y) = (x² - y², 2xy) and A consisting of all (x,y) with x > 0.

The attempt at a solution

I've tried considering the boundary, but I find that it just gets rather confusing. Is there a simpler way of doing problems like this? Btw, how would considering the boundary even work? Couldn't the image go really crazy? But continuity and differentiability probably guarantee the function is pretty well behaved eh?

Thanks for the help!

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# Finding the image of a set under f?

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