Question

How do you determine whether a function is odd, even, or neither: `h(x)=x/(x^2-1)`?

Answer 1

`h(x)` is an odd function.

Explanation:

A function is even if `f(-x)=f(x)` and if `f(-x)=-f(x)`, the function is odd. If `f(-x)` is not equal to either `f(x)` or `-f(x)`, it is neither odd nor even.

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

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

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

= `-h(x)`

Hence `h(x)` is an odd function.