How to determine whether a function is odd or even in a positive domain

Question

We know that a function f is even if $f(-x)=f(x)$ and odd if $f(-x)=-f(x)$.
Now my question : if the domain of the function is positive number, then how can I determine whether it odd or even?

For example: determine whether the following function is odd or even.
$$f(x)=x(10-x), 0<x<10$$

score 6 · Accepted Answer · answered Jul 28 '16 at 10:56

6

It doesn't make sense to ask if a function is odd/even when the domain of definition isn't symmetric around the origin.

answered Jul 28 '16 at 10:56

mrf

43,639

thank you for your kind answer (+1) – user356595 Jul 28 '16 at 11:08
You could define something similar: odd/even around $x=5$ (which would be the same as the function $f(x+5)$ being odd/even in the usual sense). – smcc Jul 28 '16 at 11:34

How to determine whether a function is odd or even in a positive domain

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