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Math homework challenge

  • #1

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

 

Answers and Replies

  • #2
761
13
What's your attempt at finding a solution?
 
Last edited:
  • #3
change x to tan(x)
 
  • #4
761
13
Are the brackets in the right place? It seems to me that you're missing some. Furthermore is this the entire question?
 
  • #5
would you like to know the answer
 
  • #6
761
13
Yes please!
 
  • #7
f(x)=2xxxx+3xx-1/3x-3xxx it was a question of the iranian mathematical olympiad note xx means x power two
 
  • #8
761
13
So you mean: [tex]
f(x)=2x^4+3x^2- \frac{1}{3} x-3x^3
[/tex]
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?
 
Last edited:
  • #9
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
 
  • #10
761
13
Is there a website or so where I can see the question and the answers of the previous question?
 
  • #11
rock.freak667
Homework Helper
6,230
31
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

:biggrin:
 
  • #12
a geometric proof
 
  • #13
sorry!!!!!
 

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