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Turkish NMO First Round - 2012 Problem - 07 {Algebra}

Source:

July 1, 2012
function

Problem Statement

How many f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} are there satisfying f(x)f(y)f(z)=12f(xyz)−16xyzf(x)f(y)f(z)=12f(xyz)-16xyz for every real x,y,zx,y,z?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 0<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 2 \qquad <span class='latex-bold'>(C)</span>\ 1 \qquad <span class='latex-bold'>(D)</span>\ 0 \qquad <span class='latex-bold'>(E)</span>\ \text{None}
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