Definition:Even Function

Definition

Let $X \subset \R$ be a symmetric set of real numbers:

$\forall x \in X: -x \in X$

A real function $f: X \to \R$ is an even function if and only if:

$\forall x \in X: \map f {-x} = \map f x$

Also known as

An even function is also seen referred to as a symmetric function.

However, that usage is not recommended on $\mathsf{Pr} \infty \mathsf{fWiki}$ as there are other concepts which bear that name.

Also see

• Definition:Odd Function

• Results about even functions can be found here.

Sources

• 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter One: $\S 4$. Even and Odd Functions: $(1)$
• 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(h)}$ Even and Odd Functions
• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $1$. Functions: $1.5$ Trigonometric or Circular Functions: $1.5.2$ Sine Function
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): symmetric function: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): even function