Question

How do you determine if `f(x)=6x-root3x` is an even or odd function?

Answer 1

This `f(x)` is an odd function since `f(-x) = -f(x)` for any `x`.

Explanation:

`f(x)` is an even function if `f(-x) = f(x)` for any `x`

`f(x)` is an odd function if `f(-x) = -f(x)` for any `x`

For any value of `x` we have:

`f(-x) = 6(-x)-root(3)(-x) = -6x+root(3)(x) = -(6x-root(3)(x)) = -f(x)`

So `f(x)` is an odd function.