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The set of implicit functions covers a certain function-space - the set of all functions that can be represented by an implicit relation. Parametric functions also covers a function-space, that at least overlaps implicit functions in some points.

Is it the case that every implicit function can be converted to a parametric form? Or are there implicit functions that cannot be represented as a parametric function, and vice versa? Is the set of implicit functions a subset of parametric functions?