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## Homework Statement

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

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- Thread starter hadi amiri 4
- Start date

- #1

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

- #2

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What's your attempt at finding a solution?

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- #3

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change x to tan(x)

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- 761

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- #5

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would you like to know the answer

- #6

- 761

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Yes please!

- #7

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- #8

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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?

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?

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- #9

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------->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

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

- #11

rock.freak667

Homework Helper

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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

- #12

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a geometric proof

- #13

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sorry!!!!!

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