Question

How do you know if `h(x) = x / (x^2 - 1)` is an even or odd function?

Answer 1

Examine `h(-x)` to see that `h(x)` is an odd function.

Explanation:

A function `f(x)` is even if `f(-x) = f(x)`.
A function `f(x)` is odd if `f(-x) = -f(x)`

Then, to see if `h(x)` is even or odd, we examine `h(-x)`.

`h(-x) = (-x)/((-x)^2-1)`

`= -x/(x^2-1)`

`= -h(x)`

Thus `h(x)` is odd.