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SuicideFuel Problem (The easiest one from Brazil's hardest entrance exam)

trying to ascend

trying to ascend

Oldcel KHHV
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Be f: D-->IR a function where D = (x belonging to IR/ X is different from 0 and 1) and that satisfies the equation f(x - 1/x) + f(x) - x + 2 = 0.

The value of f(2) is?
 
IME, since the math exam, especially the written one, is harder than ITA's one. But overall, both are in a similar level if we take in account the whole test, though the competition makes ITA harder to pass
 
incel and brainlet, worst combo ever
 
can you solve it without looking it up?
 

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