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Iran TST

Source: Iranian TST 2019, first exam day 2, problem 5

April 10, 2019
functionalgebraTSTIranIranian TSTfunctional equation

Problem Statement

Find all functions f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} such that for all x,y∈Rx,y\in \mathbb{R}: f(f(x)2−y2)2+f(2xy)2=f(x2+y2)2f\left(f(x)^2-y^2\right)^2+f(2xy)^2=f\left(x^2+y^2\right)^2
Proposed by Ali Behrouz - Mojtaba Zare Bidaki
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