Thread: Extend a function to an impair one.

1. Extend a function to an impair one.

Hello, I have been ask to extend the following function to [-1,1] such that the new functions becomes impair. The problem is that I dont know how to do it. Thanks!

2. Re: Extend a function to an impair one.

Originally Posted by orbit
Hello, I have been ask to extend the following function to [-1,1] such that the new functions becomes impair. The problem is that I dont know how to do it. Thanks!
In Spanish, función impar is equivalent in English to odd function so, I suppose you mean becomes odd instead of becomes impair . In such a case the problem has no solution because if $f$ is odd then, $f(-0)=-f(0)\Rightarrow f(0)=0$ .

3. Re: Extend a function to an impair one.

Originally Posted by FernandoRevilla
In Spanish, función impar is equivalent in English to odd function so, I suppose you mean becomes odd instead of becomes impair . In such a case the problem has no solution because if $f$ is odd then, $f(-0)=-f(0)\Rightarrow f(0)=0$ .
Hello,

thanks. The correct word is odd.

And thanks for letting me know the problem has no solution. The correct question is now available.

4. Re: Extend a function to an impair one.

Originally Posted by orbit
Hello, I have been ask to extend the following function to [-1,1] such that the new functions becomes impair. The problem is that I don`t know how to do it. Thanks!
This is the correct question. Sorry!

5. Re: Extend a function to an impair one.

Originally Posted by orbit
This is the correct question. Sorry!
Try it. Remember, $f:[-a,a]\to \mathbb{R}$ is odd iff $f(-x)=-f(x)$ for all $x\in [-a,a]$ .