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In mathematics, to give a function f implicitly is to give an equation R(x,y) = S(x,y) that at least in part has the same graph as y = f(x). It can be useful to define a function f implicitly when there is no simple formula for f(x) so it is not convenient to give its graph in the form y = f(x). If there is a way to rearrange the implicit equation, making the left hand side be y and the right hand side be a formula in x with no y, then the function can be explicitly defined.
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