Math homework challenge

[hadi amiri 4]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[dirk_mec1]

What's your attempt at finding a solution?

 

[hadi amiri 4]

change x to tan(x)

 

[dirk_mec1]

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

 

[hadi amiri 4]

would you like to know the answer

 

[dirk_mec1]

Yes please!

 

[hadi amiri 4]

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

 

[dirk_mec1]

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?

 

[hadi amiri 4]

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

 

[dirk_mec1]

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

 

[rock.freak667]

what about this one
prove that: Arctan(1)+Arctan(2)+Arctan(3)=Pi

I can actually do this one...haha

just use tan(A+B+C) where tanA=1,tanB=2,tanC=3

 

[hadi amiri 4]

a geometric proof

 

[hadi amiri 4]

sorry!!!!!