Examples of Odd Function
Some examples of odd functions are listed as follows:
- sin x
- tan x
- x2n+1, where n is a natural number
- sin3x
- tan 3x
- sinh x
Note: To check for an odd function, substitute -x in place of x in the expression of f(x), if the obtained expression is equivalent to -f(x), the function is an odd function otherwise not.
Example: Check whether f(x) = x3 is an odd function or not.
Given,
- f(x) = x3
Substituting -x in place of x in f(x), we get,
⇒ f(-x) = (-x)3 = -x3 = -f(x)
Thus, we get f(-x) = -f(x)
Hence, f(x) is an odd function.
Odd Function-Definition, Properties, and Examples
Odd Function is a type of function that follows the relation f(-x) equals -f(x), where x is any real number in the domain of f(x). This implies that odd functions have the same output for positive and negative input but with an opposite sign. Due to this property, the graph of an odd function is always symmetrical around the origin in cartesian coordinates. Also, this property of odd functions helps one to derive further mathematical relations and get implications for physical quantities expressed by odd functions.
In this article, we will learn about odd functions, their examples, properties, graphical representation of odd functions, some solved examples, and practice questions related to odd functions.