- #1
canopus
f(x)+2*f((x+2000)/(x-1))=4011-x ---> f(x)=?
f(x)+2*f((x+2000)/(x-1))=4011-x ---> f(x)=?
f(x)+2*f((x+2000)/(x-1))=4011-x ---> f(x)=?
F(x)+2*f((x+2000)/(x-1))=4011-x -> f(x)=?
- Context: Graduate
- Thread starter canopus
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Discussion Overview
The discussion revolves around the functional equation f(x) + 2*f((x+2000)/(x-1)) = 4011 - x, with participants exploring methods to solve for f(x). The scope includes mathematical reasoning and problem-solving strategies, with some participants expressing uncertainty about how to approach the problem.
Discussion Character
- Exploratory, Homework-related, Mathematical reasoning, Debate/contested
Main Points Raised
- Some participants suggest rewriting the equation to isolate f(x), proposing f(x) = 4011 - x - 2f((x+2000)/(x-1)).
- Others express frustration about the lack of initial context or attempts to solve the problem, suggesting that sharing what has been tried could facilitate better assistance.
- A participant proposes finding a specific x that simplifies f((x+2000)/(x-1)) to f(x) as a potential approach.
- Another participant mentions a different functional equation involving f((x-3)/(x+1)) + f((3+x)/(1-x)) = x, indicating a desire to explore linear functions as a solution method.
- Some suggest trial solutions, such as f(x) = ax + b or f(x) = ax^2 + bx + c, to find constants that satisfy the equation.
- There is a question about the nature of the function being sought, with participants wondering if it could be geometric, quadratic, or rational.
- One participant attempts to solve for x by manipulating the equation, but notes that the reasoning appears circular.
- Another participant expresses a desire to develop their mathematical skills rather than seeking homework help, indicating a broader interest in learning.
Areas of Agreement / Disagreement
Participants do not reach a consensus on how to solve the functional equation, with multiple approaches and viewpoints presented. There is a mix of suggestions, frustrations, and attempts to clarify the problem without a clear resolution.
Contextual Notes
Some participants note the importance of context in solving the equation, such as the need for additional equations to solve for both x and f(x). There is also mention of the lack of clarity regarding the type of function being investigated, which may affect the approach taken.
Who May Find This Useful
This discussion may be useful for individuals interested in functional equations, mathematical problem-solving strategies, and those looking to engage in collaborative learning within a mathematical context.
- #2
Nenad
- 698
- 0
[tex]f(x) = 4011 - x - 2f((x+2000)/(x-1))[/tex] lol
you can't just ask a quastion and expec to get a straight up answer. Its not done that way here. Tell me what you have so far, and where you are stuck.
you can't just ask a quastion and expec to get a straight up answer. Its not done that way here. Tell me what you have so far, and where you are stuck.
- #3
canopus
If i could solve it, i wouldn't have written here! How can we annihilate f((x+2000)/(x-1)), i guess we should equalize it to f(x), but how?
- #4
canopus
Oops! Maybe, i should write this question in ''homework'' or something like that part. Sorry for that!
- #5
Muzza
- 689
- 1
Even a little "help, I don't even know how to start this problem" in the first post goes a long way towards getting people to not feel like you're just using them.
Anywho, suppose that you could find an x so that f((x+2000)/(x-1)) could be simplified to just f(x), i.e. a solution y to (y+2000)/(y-1) = x... Maybe that hint will help.
- #6
canopus
-
Thats the difficulty of learning English! Again, sorry, if i was rude.
By the way i finally solved the problem, but one more thing... Another function... The question is; f ((x-3)/(x+1))+f((3+x)/(1-x))=x ---> f(x)=?
I showed that (x-3)/(x+1)=a and -(x+3)/(1-x)=a' ---> f'(a)=b, f(b)=a,
f(a)+f(b)=x can i use linear function to continue the solution?
Thats the difficulty of learning English! Again, sorry, if i was rude.By the way i finally solved the problem, but one more thing... Another function... The question is; f ((x-3)/(x+1))+f((3+x)/(1-x))=x ---> f(x)=?
I showed that (x-3)/(x+1)=a and -(x+3)/(1-x)=a' ---> f'(a)=b, f(b)=a,
f(a)+f(b)=x can i use linear function to continue the solution?
- #7
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
- 10,165
- 138
First, make a trial solution f(x)=ax+b.
If you can find constants a,b such that the equation is valid for every x, then you have found a solution of your functional equation.
(It is by no means certain that you have found every solution)
If the above approach doesn't work, try another trial solution f(x)=ax^2+bx+c
Good luck!
If you can find constants a,b such that the equation is valid for every x, then you have found a solution of your functional equation.
(It is by no means certain that you have found every solution)
If the above approach doesn't work, try another trial solution f(x)=ax^2+bx+c
Good luck!
- #8
- #9
Alkatran
Science Advisor
Homework Helper
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canopus said:
Question: What kind of function is this? Is it geometric, quadratic, 5th degree, rational? (What are you currently studying in math? That information can narrow down the possibilities)
Also, don't you need two equations if you're going to solve for x AND f(x) ? Couldn't you just say "f(x) = 0 and x = 4011" and save yourself some time?
- #10
Nenad
- 698
- 0
NickyuTse said:
do not post answers like that. Hints are fine, answers are not.
- #11
Alkatran
Science Advisor
Homework Helper
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From that picture:
x=(x+2000)/(x-1)
x^2-x = x+2000
x^2-2x-2000 = 0
x = (2 +- sqr(4 - 4*1*-2000))/2 = 1 +- sqr(-7996) = 1 +- 89.4
He assigned a value to x to solve the problem. Although half of the work there doesn't make any sense since it seems to go in circles.
f(91.4) + 2*f(91.4) = 4011 - 91.4
After that it's sortof... very... easy.
x=(x+2000)/(x-1)
x^2-x = x+2000
x^2-2x-2000 = 0
x = (2 +- sqr(4 - 4*1*-2000))/2 = 1 +- sqr(-7996) = 1 +- 89.4
He assigned a value to x to solve the problem. Although half of the work there doesn't make any sense since it seems to go in circles.
f(91.4) + 2*f(91.4) = 4011 - 91.4
After that it's sortof... very... easy.
- #12
canopus
''Question: What kind of function is this? Is it geometric, quadratic, 5th degree, rational?'' --> It wasn't clarified in the question. When it comes to me, i just learned second degree. These are not homeworks of course, i just want to devolop myself. And again sorry for that, i don't know the rules here.
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