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Functional Equation

Source: Iran MO 3rd round 2016 finals - Algebra P3

September 1, 2016
algebrafunctional equationfunctionIran

Problem Statement

Find all functions f:R+ā†’R+f:\mathbb {R}^{+} \rightarrow \mathbb {R}^{+} such that for all positive real numbers x,y:x,y:
f(y)f(x+f(y))=f(x)f(xy)f(y)f(x+f(y))=f(x)f(xy)
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