Function of a real variable
Implicit functions

A real-valued implicit function of a real variable is not written in the form " y = f (x)". Instead, the mapping is from the space R {\displaystyle \mathbb {R} } to the zero element in R {\displaystyle \mathbb {R} } (just the ordinary zero 0):

and

is an equation in the variables. Implicit functions are a more general way to represent functions, since if:

then we can always define:

but the converse is not always possible, i.e. not all implicit functions have the form of this equation.
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