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Find all functions \(f:\mathbb R \to \mathbb R\) that satisfy \(f(x) + f \left( \frac{x - 1}{x} \right) = \frac{5x^2 - x - 5}{x}\) for all nonzero x.

 Apr 15, 2020
 #1
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f(x) = (2 + 3x)/x.

 
 Apr 15, 2020
 #2
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Could you explain to me how you got that answer?

I want to learn the tactics that you used to derive it.

 
 Apr 15, 2020
 #3
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Deleted.  See below

 

(Clearly f(x) = (2 + 3x)/x is incorrect.)

 
 Apr 15, 2020
edited by Alan  Apr 16, 2020
 #4
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alan, according to my calculations i believe the only possible answer is fx=5x-3!!!

 
Guest Apr 15, 2020
 #5
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You are right!  In fact, if you look at my f(x)+f((x-1)/x) it doesn't equal g(x), there is multiplier of 5 that shouldn't be there!!

 
Alan  Apr 15, 2020

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