Let R be an integral domain with quotient field F, let S be a non-empty subset of R and let n = 2 be an integer. If there exists a rational function ?: S [right arrow] F such that ?(a)[superscript n] = a for all a ? S, then S is finite. As a consequence, if F is an ordered field (for instance,[real numbers]) and S is an open interval in F, no such rational function ? exists. Applications to finite fields and additional examples are given. The methods used are algebraic. A closing remark indicates how this note could be used as enrichment material in courses ranging from precalculus to undergraduate courses on abstract algebra or analysis.