Even and Odd Functions Examples
Example 1: Using the notion of even and odd functions, ascertain if the function f(x) = Cosh(x) is even or not.
Solution:
Given Function:
- f(x) = Cosh(x)
f(x) = f(-x) for all x in its domain
Cosh(x) = Cosh (-x)
Cosh(-x) = Cosh (x)
Cosh(x), satisfies the condition f(x) = f(-x)
So, therefore, Cosh(x) is an even function
Example 2: Identify whether the function f(x) = x4 + 2x2 -3 is even, odd, or neither.
Solution:
For Even Function:
Let’s take f(-x)
f(-x) = (-x)4 +2(-x)2 – 3
f(-x) = x4 + 2x2 – 3
Since, f(x) = f(-x),
Therefore, function f(x) is even.
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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