Question

How do you know if `f(x)= 6x^3 - 2x` is an even or odd function?

Answer 1

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

Explanation:

To find out we need to test out how the value of `f(-x)` is compared to `f(x)`. According to https://en.wikipedia.org/wiki/Even_and_odd_functions

if `f(x)=f(-x) ->` this is an even function.
if `f(-x)=-f(x) ->` this is an odd function.

So let's see what happens if you input (-x) in f(x):
`f(-x)=6(-x)^3-2(-x)`
`=-6x^3+2x`
`=-(6x^3-2x)`
`=-f(x)`

Conclusion, our function is odd.