# Math homework challenge

## Homework Statement

suppose f(x-1/x+1)+f(-1/x)+f(1+x/1-x)=x then find f(x)

## The Attempt at a Solution

What's your attempt at finding a solution?

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change x to tan(x)

Are the brackets in the right place? It seems to me that you're missing some. Furthermore is this the entire question?

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

So you mean: $$f(x)=2x^4+3x^2- \frac{1}{3} x-3x^3$$
This isn't possible the function is defined for 1, -1 and 0 and the exercise says that that isn't possible.

What method did they use to get the solution other than just trying different order of polynomials? Can you give me the website where you got this?

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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
prove that: Arctan(1)+Arctan(2)+Arctan(3)=Pi

Is there a website or so where I can see the question and the answers of the previous question?

rock.freak667
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