What are Even and Odd Functions?
In mathematics, there are various kinds of functions that we examine. We can use algebra or graphics to determine whether a function is even or odd. Whereas, if a function f(x) meets the following condition for every x in its domain:
f(x) = f(-x), then it is considered even
On the other side, if a function f(x) meets the following condition for every x in its domain:
f(x) = -f(-x), then it is considered odd
Even and Odd Functions Definition
A real-valued function is regarded as even or odd that is symmetrical. Plugging (-x) in place of x in the function f(x) allows us to detect if a function is even or odd. Therefore, we may determine the type of function by looking at the output value of f(-x).
So, let’s see the following definitions that are given below:
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