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f( x^2 + f(y) - y ) = (f(x))^2 - f(y)

Source: 2006 VMEO III Shortlist SL A1 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 3, 2021
algebrafunctional equationfunctional

Problem Statement

Find all functions f:R→Rf:R \to R such that f(x2+f(y)−y)=(f(x))2−f(y)f(x^2+f(y)-y) =(f(x))^2-f(y) for all x,y∈Rx,y \in R
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