An example is given to show that the standard procedure for finding the inverse function of a given one-to-one function f can lead a careless student to an incorrect answer for the domain of f⁻¹. We indicate the mathematical reason that this kind of inattentive application of the standard procedure may lead to such errors. We illustrate how to tweak the standard procedure in order to produce a more complete method that invariably leads to the correct answer to such questions. The discussion also includes some historical and pedagogical comments.

function, domain, range, one-to-one function, natural domain, inverse function.