Question

How do you determine if `f(x)= (-2x³)/(7x²+8)` is an even or odd function?

Answer 1

The function is odd.

Explanation:

To check if any function is even or odd (or none!), you simply have to evaluate it in `-x`. There are three possible scenarios:

• If `f(-x)=f(x)`, then the function is even;
• If `f(-x)=-f(x)`, then the function is odd;
• If none of the two above is true, then the function is not even nor odd.

In this case, we have

`f(-x) = (-2(-x)^3)/(7(-x)^2+8)`

Since `(-x)^3=-x^3` and `(-x)^2=x^2`, the function becomes

`-(-2x^3)/(7x^2+8)`

which is exactly `-f(x)`! Thus, the function is odd.