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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 don`t know how to do it. Thanks!

Re: Extend a function to an impair one.

Quote:

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!

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 $\displaystyle f$ is odd then, $\displaystyle f(-0)=-f(0)\Rightarrow f(0)=0$ .

Re: Extend a function to an impair one.

Quote:

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 $\displaystyle f$ is odd then, $\displaystyle f(-0)=-f(0)\Rightarrow f(0)=0$ .

Hello,

thanks. The correct word is odd.

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

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Re: Extend a function to an impair one.

Quote:

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!

Re: Extend a function to an impair one.

Quote:

Originally Posted by

**orbit** This is the correct question. Sorry!

Try it. Remember, $\displaystyle f:[-a,a]\to \mathbb{R}$ is odd iff $\displaystyle f(-x)=-f(x)$ for all $\displaystyle x\in [-a,a]$ .