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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
 

#3 2011-07-22 21:15:24

Thanh Vân
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Re: Function

Oh. I have find


Please pose your proof?

 

#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
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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
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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
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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
 

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