Suppose $f$  is a function, with domain $D$ and $G(x,y)$ is a function of $x$ and $y$ that appears in the equation, $G(x,y) = 0$.
Definition:We say that $f$ is an implicit function for the equation $G(x,y) =0$ if (and only if) for every $x \in D, G(x,f(x))=0$.

Graph of Implicit Function for
                x^2+y^2 -4 = 0
              Diagram for Implicit Function for x^2+y^2-4=0
Diagram IMPL Graph and Mapping Diagram for $f$ as an implicit function for $G(x, y)=x^2+y^2-4=0$