Properties of an Odd Function
Odd Function have following properties:
- Addition and Subtraction of two odd functions is an odd function.
- Product of two odd functions is an even function.
- Product of an odd function and an even function is an odd function.
- Graph of an odd function exhibits rotational symmetry about origin in cartesian coordinates system.
- Average value of odd functions over a symmetric interval around the origin is zero.
- For any odd function, f(-x) = -f(x).
- Composition of two odd functions is an odd function.
- Definite integral of an odd function about a symmetric interval around origin is zero. i.e.
∫-aa f(x).dx = 0
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.