In
mathematics, more specifically in
multivariable calculus, the
implicit function theorem is a tool that allows relations to be converted to
functions of several real variables. It does so by representing the relation as the
graph of a function. There may not be a single function whose graph is the entire relation, but there may be such a function on a restriction of the
domain of the relation. The implicit function theorem gives a sufficient condition to ensure that there is such a function.