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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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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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'

I'm not crazy, my mother had me tested.

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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****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

You are welcome.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

What about it?

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

So?

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