# Functional Equations

**Algebra**Level pending

Let \(S\) be the set of all non-zero real-valued functions \(f\) defined on the set of all real numbers such that \[f(x^2+yf(z))=xf(x)+zf(y)\]

Find the maximum value of \(f(69)\), where \(f \in S\).

Let \(S\) be the set of all non-zero real-valued functions \(f\) defined on the set of all real numbers such that \[f(x^2+yf(z))=xf(x)+zf(y)\]

Find the maximum value of \(f(69)\), where \(f \in S\).

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