A functional equation specifies a function through an identity involving values of that function at several arguments.
If is continuous and is an additive function, then . Additivity proves this first for nonnegative rational numbers; because is continuous, the identity extends to every nonnegative real number.
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A **functional equation** is an equation in which the unknowns are functions, rather than simple variables. These equations establish a relationship between the values of functions at different points. Functional equations often arise in various fields of mathematics and can be used to characterize specific functions or sets of functions.
