Question

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

Answer 1

You substitute `-x` in place of `x` everywhere. If `f(-x)=-f(x)`, as in the case of the given function, it is odd.

Explanation:

`f(-x) = 2(-x)^3+6(-x)`

`= 2(-x^3)-6x`
`=-2x^3-6x`
`=-(2x^3+6x)`
`=-f(x)`

Note : This particular function can be easily recognized as odd in one glance, as it comprises of only odd powers of `x`