Math homework challenge

1. The problem statement, all variables and given/known data
suppose f(x-1/x+1)+f(-1/x)+f(1+x/1-x)=x then find f(x)


2. Relevant equations



3. The attempt at a solution

 

change x to tan(x)

 

would you like to know the answer

 

f(x)=2xxxx+3xx-1/3x-3xxx it was a question of the iranian mathematical olympiad note xx means x power two

 

t=x-1/x+1 ------ > tx +t=x-1 -------- >x=1+t/1-t , -1/x=t-1/t+1 ,1+x/1-x=-1/t

------->f(t)+f(t-1/t+1)+f(-1/t)=1+t/-t -------->f(x)+f(x-1/x+1)+f(-1/x)=1+x/1-x

then
t=-1/x --------->x=-1/t , x-1/x+1=t+1/1-t , 1+x/1-x=t-1/t+1
------->f(t+1/1-t)+f(t)+f(t-1/t+1)=-1/t >f(x+1/1-x)+f(x)+f(x-1/x+1)=-1/x

then
t=1+x/1-x----------->t-tx=1+x ----->x=t-1/1+t------ > -1/x =t+1/1-t , x-1/x+1=-1/t
------>f(-1/t)+f(t+1/1-t)+f(t)=t-1/t+1------->f(-1/x)+f(x+1/1-x)+f(x)= x-1/x+1

two more step remains that i think you can do them yourself
what about this one
prove that: Arctan(1)+Arctan(2)+Arctan(3)=Pi

 

a geometric proof

 

sorry!!!!!