Question

who could solve this ?

Answer 1

\[f \left( \frac{ x-3 }{ x+1 } \right) + f \left( \frac{ 3+x }{ 1-x } \right) = x\]
\[x \neq 1, x \neq -1\]
determine the function f(x)
???

Answer 2

It's kinda \(f(a)+f(-a)=x\)

Answer 3

not that simple i think..

Answer 4

u just have to skip the f(...) in the equation
then u got f(x)=(x-3)/(x+1)+(3+x)/(1-x)
simpleize it and BAM u got function f(x)

Answer 5

If you plug in 0 for x, you get f(3)+f(-3)=0 which must mean that it's an odd function.

Answer 6

Kinda.

Answer 7

odd??? why?

Answer 8

Well, f(x)=-f(-x) is what odd functions do. Also, try plugging in x=3 and x=-3 to get a couple more interesting formulas out.

Answer 9

wow :D

Answer 10

It's not too hard to show f(0)=0 and f(3)=-f(-3) but I'm sure there's more.

Answer 11

Plug in -x everywhere you see x. That'll be awesome.

Answer 12

i got out x^3 + 7x =0 :( don't know how this connect to f(x)

Answer 13

but guys the markscheme state that the answer is \[f(x) = \frac{ 4x }{ 1-x^2 } - \frac{ 1 }{ 2 }\]
???

Answer 14

i got f(x)=8x/(1-x^2) :P

Answer 15

damn it :(( whyyyy????