MathDB

Functional Equation: $f(x^2) - yf(y) = f(x + y)(f(x) - y)$.

Source: 2019 Pan-African Shortlist - A3

January 18, 2021

algebrafunctional equationfunction

Problem Statement

Find all functions

f: \mathbb{R} \to \mathbb{R}

such that

f\left(x^2\right) - yf(y) = f(x + y) (f(x) - y)

for all real numbers

x

and

y