TR-MO-R1 2012 Problem 7

Tüm $x$ , $y$ , $z$ gerçel sayıları için $f(x)f(y)f(z) = 12f(xyz) - 16xyz$ koşulunu sağlayan kaç $f : \mathbf{R} \to \mathbf{R}$ fonksiyonu vardır?

a) $3$ b) $2$ c) $1$ d) $0$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 3. Quoted with source.

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