Abstract
Functional equations are equations in which functions rather than numbers are unknown. Functional equations in the proper sense are built with the aid of elementary functions, operations, and substitutions. A classical functional equation is Cauchy's equation: f(x + y) = f(x) +f(y). The f is a function whose value at x + y is the same as its value at x added to its value at y. This should be true whatever real values x and y take on or only for positive or nonnegative values of x and y. Evidently, f (x) = c x satisfies this equation as c (x + y) = cx + cy for every real constant c.
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