Function

Thanh Vân · 2011-07-20 15:43:17

Find the function

such that

anonimnystefy · 2011-07-20 23:47:00

hi Thanh Van

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

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

Thanh Vân · 2011-07-21 23:15:24

Oh. I have find

Please pose your proof?

anonimnystefy · 2011-07-22 00:48:17

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)

Thanh Vân · 2011-07-22 02:51:01

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

anonimnystefy · 2011-07-22 02:56:08

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

anonimnystefy · 2011-07-23 00:14:58

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

Thanh Vân · 2011-07-23 17:15:30

Can you completed your proof for my problem?Thanks.

anonimnystefy · 2011-07-23 21:39:49

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.

Math Is Fun Forum

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

Function

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

Re: Function

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

Re: Function

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

Re: Function

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

Re: Function

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

Re: Function

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

Re: Function

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

Re: Function

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

Re: Function

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