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Investigate whether or not the system

$ u(x,y,z) = x+xyz $

$ v(x,y,z) = y + xy $

$ w(x,y,z) = z+2x+3z^2 $

can be solved for $x,y,z$ in terms of $u,v,q$ near $(x,y,z) = (0,0,0)$

I'm not really sure how to even start on this question. I am not looking for someone to give me a full answer, but I just want some guidance on where to start.

user100925
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  • Did you learn inverse function theorem or implicit function theorem? –  Oct 16 '13 at 22:28
  • I don't really have a good understanding of them. Especially inverse function theorem. I found this for implicit though, http://www.youtube.com/watch?v=xtgTckGMuWE – user100925 Oct 16 '13 at 22:45
  • Basically the incerse function theorem says that if $F: \mathbb R^n \to \mathbb R^n$ such that $f(p) = q$ and $Df_p$ is nonsingular, then $F$ is locally invertible. –  Oct 16 '13 at 23:25

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