Question

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

Answer 1

`x/(x^2-1)` is an odd function

Explanation:

• An even function is one for which `f(-x) = f(x)` for all `x` in the domain.

• An odd function is one for which `f(-x) = -f(x)` for all `x` in the domain.

In our example:

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

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

So `x/(x^2-1)` is an odd function.

graph{x/(x^2-1) [-10, 10, -5, 5]}