Question

How do you determine if `f(x) = (x^3 - x)/(x^3 - 4x)` is an even or odd function?

Answer 1

`f(x)` is even.

Explanation:

If a function is odd, then `f(-x)=-f(x)`. If a function is even, then `f(-x)=f(x)`. Plugging in `-x` into the given function gives

`f(-x)=((-x)^3-(-x))/((-x)^3-4(-x))=(-(x^3-x))/(-(x^3-4x))=f(x)`

Hence `f(x)` is even.