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..