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The name "functional equation" is used for problems where the goal is to find all functions satisfying the given equation (and maybe some other conditions). So in this case, solving the equation means finding all functions fulfilling the equation. (This is different from the more common use of the word equation, where the solutions are numbers.)

The term functional equation is used for problems where the goal is to find all functions satisfying given equation (and maybe some other conditions, e.g. the goal can be to find all continuous solutions). So in this case, solving the equation means finding all functions fulfilling the equation and the additional conditions. (This is different from the more common use of the word equation, where the solutions are numbers.)

A common technique used in solving functional equations is finding some properties of the solution by plugging some special values into the equation.

Some well-known functional equations are:

More information can be found at Wikipedia.

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