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Expert-verified Found in: Page 669 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # What is the definition of an odd function? An even function?

A function f is an odd function if $f\left(-x\right)=-f\left(x\right)$ for all x in the domain of f.

A function f is an even function if $f\left(-x\right)=f\left(x\right)$ for all x in the domain of f.

See the step by step solution

## Step 1. Explain an odd function.

For a real-valued function $f\left(x\right)$, when the output value of $f\left(-x\right)$ is the same as the negative of $f\left(x\right)$, for all values of x in the domain of f, the function is said to be an odd function.

An odd function should hold the following equation $f\left(-x\right)=-f\left(x\right)$, for all values of x in the domain of the function f.

## Step 2. Explain an even function.

For a real-valued function $f\left(x\right)$, when the output value of $f\left(-x\right)$ is the same as $f\left(x\right)$, for all values of x in the domain of f, the function is said to be an even function. An even function should hold the following equation $f\left(-x\right)=f\left(x\right)$, for all values of x in the domain of the function f. ### Want to see more solutions like these? 