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

Given a continuous parametric function f : R2 -> R3 specifying a 2D

surface in 3D space, define a continuous implicit function g : R3 -> R

corresponding to the same surface.

2. Relevant equations

You’ll likely want to use the infimum function.

You can ignore the inside/outside convention: g can be everywhere

nonnegative.

3. The attempt at a solution

My thought on this is that... Since g is an implicit function and is non negative everywhere else.. Then if a point lies on the surface described by g, g(x,y,z) = 0 at that point. Since g is zero on the surface and continuous and increasing everywhere else, it must include an infimum of some sort and a modified function of f, where f(s,t) = (x,y,z).. And I'm stuck from then on..

Someone help please? Any help is appreciated..

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# Homework Help: Defining implicit function given a parametric function

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