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

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Answer 1 · 2016-07-12T10:19:05

$f$ is neither even nor odd .

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.

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