How do you determine if $y= 1/x$ is an even or odd function?

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Answer 1 · 2016-08-06T14:54:41

I'd say odd.

You can check by considering general rule:
ODD if: $f(-x)=-f(x)$
EVEN if: $f(-x)=f(x)$

So basically test a positive and a negative $x$ such as, for example:
$2 and -2$

You get:
$f(x)=f(2)=1/2=0.5$
$f(-x)=f(-2)=-1/2=-0.5$

so basically we have that:

$f(-x)=-0.5=-f(x)$

giving an ODD function.

How do you determine if y= 1/xy= 1/x is an even or odd function?