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Understanding Symmetry in Equations: Even and Odd Functions

In the realm of mathematics, the concept of symmetry plays a crucial role in analyzing and understanding functions. This article explores the symmetries in equations by focusing on even and odd functions. Let's break down these concepts to gain a clearer insight into their characteristics and implications.

Even Functions

An even function is defined by the property that for any input ( x ), the function's output is the same when using the negative of that input. Mathematically, this can be expressed as:

[ f(-x) = f(x) ]