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**juxta****Member**- Registered: 2012-05-19
- Posts: 2

Hello everyone, its has been a while since i last visited. I have a small problem on functions at the moment, I looked over the internet but couldn't find the solution to this small problem. So here is the problem, in the picture below:

Is this a valid function? Where 'b' can go twice to the range? I looked at the answers from my question sheet and it said it is not a surjection :S

Kind Regards

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,458

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

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It is not a function.

A function is a relation that relates every element of the domain to exactly one element of the co-domain.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**juxta****Member**- Registered: 2012-05-19
- Posts: 2

THANK YOU SO MUCH! Thanks for the link as well, didn't know about this.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,458

You are welcome.

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

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,637

What does it being surjective have anything to do with it being a function? Anyway, to tell if it is a surjective function, we need it's codomain.

Agnishom wrote:

It is not a function.

A function is a relation that relates every element of the domain to exactly one element of the co-domain.

No, you mean range or image.

*Last edited by ShivamS (2014-05-20 08:02:38)*

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Range is that subset of the codomain which consists of all those and only all those elements on which something has been mapped.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,637

What about it?

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,637

As an added note, you are assuming that all functions are surjective. That is not the case.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,637

So?

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