Question

How do you determine if `g(x)=-3x^3+5` is an even or odd function?

Answer 1

See explanation.

Explanation:

This function is neither odd nor even.

To find if a function is odd or even you have to calculate `f(-x)`.

The function is:

• even if `f(-x)=f(x)`

• odd if `f(-x)=-f(x)`

If none of 2 possibilities occur then the function is neither odd nor even.

Here we have:

`f(-x)=-3*(-x)^3+5=-3*(-x^3)+5=3x^3+5`

`f(-x)` is NOT equal to either `f(x)` or `-f(x)`, so the function is neither odd or even.