Give an example of an odd function and explain algebraically why it is odd.

Question

jdoe0001 · Answer

http://www.mathsisfun.com/algebra/functions-odd-even.html

hero · Answer

A function, f(x),  is odd if after replacing x with -x you get -f(x). In short, A function is odd if f(-x) = -f(x). 

For example consider the function

$$f(x) = \frac{x}{x^2 - 1}$$

If we multiply both sides by -1 we get -f(x):

$$-f(x) = -\frac{x}{x^2 - 1}$$

So if the f(x) is odd, we should be able to get -f(x) when we replace x with -x. Let's try it:

$$f(-x) = \frac{-x}{(-x)^2 - 1}$$
$$f(-x) = -\frac{x}{x^2 - 1}$$

As you can see, we arrive at a result for f(-x) that is the same as -f(x). Therefore, the function is odd.