Question

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

Answer 1

`f` is neither even nor odd .

Explanation:

For a fun. `f` to be even , we must have, `AAx, f(-x)=f(x)`

and for odd, `f(-x)=-f(x)`

We have, with our `f`,

`f(-x)=(-x)^2+sin(-x)=x^2-sinx`

We find that, `f(-x)!=+-f(x)`

So, we conclude that given fun. `f` is neither even nor odd.