'Parity' of Functions

Algebra Level 2

We all know that by parity of integers ,

$\text{ odd number + odd number = even number } \; .$

Then $\text{ odd function + odd function }$ is always an $\text{\_\_\_\_\_\_\_\_\_\_}$ .

Clarification : The function in question is for $\mathbb R \to \mathbb R$ .

Even function Odd function

1 solution

展豪張
Mar 14, 2016

Let $f(x),g(x)$ be odd functions.
Let $h(x)=f(x)+g(x)$ .
$h(-x)=f(-x)+g(-x)=-f(x)-g(x)=-h(x)$
Thus $h(x)$ is odd function.

I love the way you solved this!

This question actually took me quite long to figure out, but I would say it's one of the most interesting ones from function related problems. ;) Good job!

Zyberg NEE - 5 years, 2 months ago

Sheesh! Pretty elegant method to solve this!

Rahadian Putra - 5 years, 2 months ago

Thanks guys ;)

展豪張 - 5 years, 2 months ago

'Parity' of Functions

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