$ f(x) = x $: $ f(a + b + c) = a + b + c = f(a) + f(b) + f(c) $, and $ f(ab) = ab = f(a)f(b) $ — OK

Tue, 05 May 2026 07:14:49 +0000

Understanding the Linear Function $ f(x) = x $: A Deep Dive into Additive and Multiplicative Properties The function $ f(x) = x $ is a cornerstone in the study of mathematics, particularly in algebra and functional equations. Simple at first glance, its behavior reveals deep and elegant properties that satisfy key mathematical identities: additivity and multiplicativity. ### The Additive Property of $ f(x) = x $ One of the most intuitive characteristics of $ f(x) = x $ is its additive property. For any real numbers $ a, b, c $, the function satisfies: