Functional equations are mathematical equations where the unknowns are functions rather than simple variables. These equations often express a relationship between the values of a function at different points. Solving functional equations typically involves finding a function that satisfies the given conditions, which can lead to discovering properties of the function itself. Common examples of functional equations include the Cauchy functional equation and the Additive Cauchy equation. These equations are used in various fields, including analysis, number theory, and combinatorics, to explore the behavior of functions and their interactions. Understanding functional equations can provide deeper insights into mathematical structures and relationships.