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#1 2011-07-20 15:43:17

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

Function

Find the function

such that

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#2 2011-07-20 23:47:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,397

Re: Function

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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#3 2011-07-21 23:15:24

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

Re: Function

Oh. I have find


Please pose your proof?

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#4 2011-07-22 00:48:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,397

Re: Function

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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#5 2011-07-22 02:51:01

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

Re: Function

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

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#6 2011-07-22 02:56:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,397

Re: Function

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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#7 2011-07-23 00:14:58

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,397

Re: Function

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.

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

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#8 2011-07-23 17:15:30

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

Re: Function

Can you completed your proof for my problem?Thanks.

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#9 2011-07-23 21:39:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,397

Re: Function

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.

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

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