An equation that relates two variables can often be used to
define one or more functions that connect the variables with the
This is what is described by saying a function is defined implicitly by an equation.
An illustration of this general statement is the connection of inverse functions examined in OW.IVPPF.Thus by examining the equation $y^2 -x =0$ we come to define two functions, $ f_+(x) =\sqrt x$ and $f_-(x)=-\sqrt x$, both of which can be substituted in the equation for $y$ to make the original equation true.
Example OW.0 also
illustrates the general way in which a function can be
defined implicitly by an equation.