Solving alternative functional equations: What for?

Abstract. To make it less abstract, answering the title question let us twist British mountaineer George Mallory's famous dictum: “Because they're there.” The article yields a counterpart of Mihály Bessenyei and Gréta Szabó's paper [3] dealing with addition formula characterizing the \(\, {\rm tanh} \,\) function. The emphasis is given on proving that a natural understanding of a solution of a functional in question requires to view that equation as an alternative one. For the most part the paper has a survey character.