An additive function is a type of mathematical function that satisfies the property of additivity. This means that for any two inputs, the function's output for their sum is equal to the sum of the outputs for each input separately. In formal terms, if f is an additive function, then f(x + y) = f(x) + f(y) for all x and y . Additive functions are commonly studied in various fields, including mathematics, physics, and economics. A well-known example of an additive function is the linear function, which can be expressed in the form f(x) = ax , where a is a constant. Understanding additive functions helps in analyzing systems where the total effect is the sum of individual contributions.