Even and Odd Functions
What is Odd and Even Function?
If f(x) = f(−x) for any x in their domain, even functions are symmetric around the y-axis. Odd functions are symmetric about the origin, meaning that for every x in their domain, f(−x) = −f(x).
How can you tell if a function is even or odd?
A function is even if f(-x) = f(x), and odd if f(-x) = -f(x) for every element in the domain of f. If it doesn’t satisfy either property, it is neither odd nor even.
What are some examples of Odd Functions?
Some examples of odd functions are:
- f(x) = x3
- f(x) = sin(x)
- f(x) = 1/x
What are some examples of Even Functions?
Some examples of odd functions are:
- f(x) = x3
- f(x) = cos (x)
- f(x) = |x|
Can functions be neither Even nor Odd?
A function is neither even nor odd if it does not meet the requirements for being either. Instances comprise either linear functions such as f(x) = x or exponential functions such as f(x) = ex.
Even and Odd Functions
Even and odd functions are types of functions. A function f is even if f(-x) = f(x), for all x in the domain of f. A function f is an odd function if f(-x) = -f(x) for all x in the domain of f, i.e.
- Even function: f(-x) = f(x)
- Odd function: f(-x) = -f(x)
In this article, we will discuss even and odd functions, even and odd function definitions, even and odd functions in trigonometry, and even and odd function graphs and others in detail.
Table of Content
- What are Even and Odd Functions?
- Even and Odd Functions Definition
- Even Function
- Even Function Examples
- Even and Odd Functions Graph
- Even Functions Graph
- Odd Function
- Odd Function Examples
- Odd Functions Graph
- Neither Odd Nor Even
- Even and Odd Functions in Trigonometry
- Properties of Even and Odd Functions
- Integral Properties of Even and Odd Functions
- Even and Odd Functions Examples
- Practice Questions on Even and Odd Functions
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