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Functional Equation!

Source: Iran 3rd round 2013 - Algebra Exam - Problem 4

September 11, 2013
functionalgebrafunctional equation

Problem Statement

Find all functions f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} such that f(0)∈Qf(0) \in \mathbb Q and f(x+f(y)2)=f(x+y)2.f(x+f(y)^2 ) = {f(x+y)}^2. (25 points)
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