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**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

Find the function

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

hi Thanh Van

i think all functions of the form f(x)=kx+n.

*Last edited by anonimnystefy (2011-07-22 00:44:02)*

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

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**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

Oh. I have find

Please pose your proof?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

hi Thanh Van

Let us look at all of the functions of the form f(x)-k*x+n then we get:

i'm not sure if there are any other solutions.if there are then i will try to find it.

*Last edited by anonimnystefy (2011-07-22 00:49:11)*

Here lies the reader who will never open this book. He is forever dead.

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

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**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

I thinks you idea is not true. We must find f(x) from its condition.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

i think you are right.i just guessed it but the function is ok.we need to find a way to get it from the condition

Here lies the reader who will never open this book. He is forever dead.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

hi Thanh Van

i forgot that the solution can also be the constant function f(x)=C.

i started doing it by first assuming that the function is multiplicative.than i substituted y=-x.i got:

f(-x^2)+f(0)=f(x-x^2)+f(-x)

than by using the assumption that the function is multiplicative i got:

f(-1)f(x^2)+f(-1)f(0)=f(-1)f(x^2-x)+f(-1)f(x)

f(x)f(x)+f(x)f(0)=f(x)f(x-1)+f(x)

With the assumption that f(x)<>0:

f(x)+f(0)=f(x-1)+1

for x=1 we get:

f(1)+f(0)=f(0)+1

f(1)=1

that is the furthest i got.sry

Here lies the reader who will never open this book. He is forever dead.

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**Thanh Vân****Member**- Registered: 2011-07-17
- Posts: 10

Can you completed your proof for my problem?Thanks.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,885

hi Thanh Van

like i said that is the most i have figured out.i don't know what to do from that point on.

Here lies the reader who will never open this book. He is forever dead.

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