Question

How do you know if `f(x)=x^4+3x^-4+2x^-1` is an even or odd function?

Answer 1

`f(x)` is neither even nor odd.

Explanation:

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

and is odd if `f(-x)=-f(x)`

As `f(x)=x^4+3x^(-4)+2x^(-1)`

`f(-x)=(-x)^4+3(-x)^(-4)+2(-x)^(-1)`

= `x^4+3x^(-4)-2x^(-1)` (as `x^(-1)` is an odd power)

Hence `f(-x)!=f(x)` as also `f(-x)!=-f(x)`

Hence, `f(x)` is neither even nor odd.