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.
f(x) = (2 + 3x)/x.
Could you explain to me how you got that answer?
I want to learn the tactics that you used to derive it.
Deleted. See below
(Clearly f(x) = (2 + 3x)/x is incorrect.)
alan, according to my calculations i believe the only possible answer is fx=5x-3!!!
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!!
