The present paper establishes a fact which, in the terminology adopted in the theory of approximation, is called the inverse theorem. The case in point is that if a function, continuous in a set, can be approximated at a given rate at some appropriate scale by some pool of approximating functions, then it has a well-defined smoothness. If, in addition, it is known that functions of smoothness considered can be approximated at a required rate, we obtain a constructive description of the smoothness class in terms of the rate of approximation.