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## #1 2011-07-21 13:43:17

Thanh Vân
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### Function

Find the function

such that

## #2 2011-07-21 21:47:00

anonimnystefy
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### Re: Function

hi Thanh Van

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

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Thanh Vân
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Oh. I have find

## #4 2011-07-22 22:48:17

anonimnystefy
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### 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 22:49:11)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #5 2011-07-23 00:51:01

Thanh Vân
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### Re: Function

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

## #6 2011-07-23 00:56:08

anonimnystefy
Real Member

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### 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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #7 2011-07-23 22:14:58

anonimnystefy
Real Member

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### 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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #8 2011-07-24 15:15:30

Thanh Vân
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### Re: Function

Can you completed your proof for my problem?Thanks.

## #9 2011-07-24 19:39:49

anonimnystefy
Real Member

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### 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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment