Question

How do you determine if `f(x)= 5x³` is an even or odd function?

Answer 1

`f(x)=5x^3` is an odd function.

Explanation:

A function `f(x)` is odd if `f(-x)=-f(x)` and it is even, if `f(-x)=f(x)`.

As `f(x)=5x^3`

`f(-x)=5(-x)^3=5×(-x^3)=-5x^3=-f(x)`

As such `f(x)=5x^3` is an odd function.