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A hard functional equation in Taiwan TST

Source: 2022 Taiwan TST Round 2 Independent Study 2-A

April 8, 2022
algebrafunctional equationmingTaiwan

Problem Statement

Determine all functions f:R+ā†’R+f: \mathbb{R}^+ \to \mathbb{R}^+ satisfying f(x+y2f(y))=f(1+yf(x))f(x)f\bigl(x + y^2 f(y)\bigr) = f\bigl(1 + yf(x)\bigr)f(x) for any positive reals xx, yy, where R+\mathbb{R}^+ is the collection of all positive real numbers.
Proposed by Ming Hsiao.
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