Properties of an Even Function
Even Functions holds the following properties:
- Addition or subtraction of two even functions is an even function.
- Product of two even functions is also an even function.
- The plot of even functions exhibit symmetry about Y-axis.
- Average value of even functions over a symmetric interval around the origin is the functional value at x=0, i.e. f(0).
- For any even function, f(-x) = f(x).
- Composition of an even and odd function is also an even function.
- Composition of two even functions is an even function.
Even Function
Even function is defined as a function that follows the relation f(-x) equals f(x), where x is any real number. Even functions have the same range for positive and negative domain variables. Due to this, the graph of even functions is always symmetric about the Y-axis in cartesian coordinates.
In this article, we will learn about even functions, their examples, properties, graphical representation of even functions, some solved examples, and practice questions related to even functions.
Table of Content
- What is an Even Function?
- Graphical Representation of an Even Function
- Properties of an Even Function
- Even Function and Odd Function Difference