Properties of Even and Odd Functions
Some of the properties of Even and Odd Functions are given below.
- Only function that has an odd and even domain made up entirely of real numbers is the constant function, f(x) = 0, which is exactly zero.
- It is even to add two even functions and odd to add two odd functions. i.e.
- Even Function + Even Function = Even Function
- Odd Function + Odd Function = Odd Function
- When two even functions are separated, the difference is even, and when two odd functions are separated, the difference is odd.
- Unless one of the functions is a zero function, the sum of an even and an odd function is neither even nor odd.
- Both the product of two odd functions and the product of two even functions are even.
- Both the quotient of two odd functions and the quotient of two even functions are even.
- When two even functions are combined, they become even, and when two odd functions are combined, they become odd.
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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