Question

How do you determine if `f(x)= X^11 + X^9` is an even or odd function?

Answer 1

`f(x)=x^11+x^9` is an odd function.

Explanation:

If `f(-x)=f(x)`, `f(x)` is an even function. And if `f(-x)=-f(x)`, `f(x)` is an odd function.

Here we have `f(-x)=x^11+x^9` and hence

`f(-x)=(-x)^11+(-x)^9=-x^11-x^9=-(x^11+x^9)=-f(x)`

As such, `f(-x)=x^11+x^9` is an odd function.