0791616e85
Fixed copy/pasting(?) typos, also changed the 'because' in each example to explain the why instead of just showing it's true for a single number, not mentioning any others. (Proof by example is very, very, VERY bad to encourage.)
30 lines
974 B
Markdown
30 lines
974 B
Markdown
---
|
|
title: Even and Odd Functions
|
|
---
|
|
## Even and Odd Functions
|
|
|
|
### General Functions
|
|
|
|
A function `f` is a mapping from a set A (input/domain) to a set B (output/co-domain).
|
|
|
|
### Even Function:
|
|
|
|
A function `f(x)` is even if and only if `f(x) = f(-x)`.
|
|
|
|
An example of an even function would be `f(x) = x^2` because `(-x)^2 = x^2`. For example, `f(2) = 2^2 = 4 = (-2)^2 = f(-2)`.
|
|
|
|
The trigonometric functions - `cos(x)` and `sec(x)` are also even functions
|
|
|
|
### Odd Function
|
|
|
|
A function `f(x)` is odd if and only if `f(x) = -f(-x)`
|
|
|
|
An example of an odd function would be `f(x) = x^3` because `(-x)^3 = -x^3`, so `-(-x)^3 = x^3`. For example, `f(2) = 2^3 = 8 = -(-8) = -(-2)^3 = -f(-2)`.
|
|
|
|
The trigonometric functions - `sin(x)`, `tan(x)`,`cot(x)` and `cosec(x)` are also odd functions
|
|
|
|
#### More Information:
|
|
<!-- Please add any articles you think might be helpful to read before writing the article -->
|
|
|
|
- [Wikipedia](https://en.wikipedia.org/wiki/Even_and_odd_functions)
|