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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

Find all functions f: (0,∞)------ (0,∞) such that

f(f(f(x))) + 4f(f(x)) + f(x) = 6x .

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

I suspect *f* has to be linear. If so, let

I dont know if *f* can be non-linear (though I have a hunch that it cant).

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Also

So f must be injective. Thats another thing we can say about the function.

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**tony123****Member**- Registered: 2007-08-03
- Posts: 189

thank you jane

but i think The only solution of function is f(x) = x,

what can be easily checked.

*Last edited by tony123 (2008-07-23 04:49:41)*

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Youre right. I just noticed that *f* is from

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