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Beautiful Disguised Functional!

Source: Pakistan TST(2). P3. Proposed by Awais Chisti and Sualeh Asif

January 28, 2017
functional equationFunctional Equationsalgebra proposedalgebraalgebraic identities

Problem Statement

Find all f:R+→R+f:\mathbb{R}^+ \rightarrow \mathbb{R}^+ such that for all distinct x,y,zx,y,z
f(x)2−f(y)f(z)=f(xy)f(y)f(z)[f(yz)−f(zx)]f(x)^2-f(y)f(z)=f(x^y)f(y)f(z)[f(y^z)-f(z^x)]
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