Question

Is the function `f(x)=x^2/(x-1)` even, odd or neither?

Answer 1

It is neither odd or even.

Explanation:

First of all if you want to discuss if a function is odd or even, the domain of the function must be symetrical to 0 (in other words if `x in D` then `-x in D`).

Function given in this task does not satisfy this condition, because `-1 in D` but `1 cancel(in) D`.

Answer 2

`f` is neither even nor odd.

Explanation:

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

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

`f(-x) != f(x)` (that is `f(-x)` is not always the same as `f(x)`), so `f` is not even

`f(-x) != -f(x)` (that is `f(-x)` is not always the same as `-f(x)`, so `f` is not odd.

`f` is neither even nor odd.