Question

How do you determine if `f(x) = root3(7x^3 - 3x)` is an even or odd function?

Answer 1

It is an odd function. A function is even if `f(-x)=f(x)` and odd if `f(-x)=-f(x)`.

Explanation:

So let's see what `f(-x)` is:

`f(-x)=root(3)(7(-x)^3-3(-x))`

`=root(3)(-7x^3+3x)=root(3)(-(7x^3-3x))=-root(3)((7x^3-3x))=-f(x)`

`f(-x)=-f(x)`, therefore it is an odd function.