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**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

Define a bijection between the sets [-2,8] and [3,5]. Prove your function is actually a bijection.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,736

hi daydoe12

Welcome to the forum.

How about

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,822

Hi daydoe12

*Last edited by anonimnystefy (2012-11-27 02:20:37)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,736

Good answer, Stefy.

I think yours is correct and I have misunderstood what is wanted.

I'll leave the post as a reminder to me to **read the question!**

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,822

Hmmm... I thought there was another reason.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,736

Which was ... ?

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,822

Doesn't matter. I hope we solved the OP's problem.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

how did you arrive at that answer

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,736

Stefy just looked for a formula of the form y = mx + c so that when x = -2, then y = 3, and similarly when x = 8, y = 5.

My answer used a similar idea but I think his is the right way.

If you think about the straight line graph this produces, every point between -2 and 8, will map onto every point between 3 and 5

And the mapping is reversible.

To prove it, you'd have to show the mapping is 1:1 in both direcctions, and that a point inside the first interval maps to a point inside the resulting interval.

Bob

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**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

anonimnystefyLegendary Memberb how did you arrive at that answer

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,822

Hi daydoe12

Bob explained very well in post #9. I don't think I could any better at explaining it.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,736

Thank you Stefy.

And there was me, about to award you the "Teacher of the Month Award"

Bob

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**daydoe12****Member**- Registered: 2012-11-18
- Posts: 8

I have tried finding the form using the y=mx+b formula and i cant figure out how she got x+17/5

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,350

Hi daydoe12;

You have -2 -> 3 and 8 -> 5 so call x=-2 and y =3 in the first equation and x = 8 and y = 5 in the second.

When you solve that you get m = 1/5 and b = 17 / 5. Now plug in to the first equation.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,822

bob bundy wrote:

Thank you Stefy.

And there was me, about to award you the "Teacher of the Month Award"

Bob

I hope you are kidding.

Hi daydoe12

I'm male, not female...

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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