Functional Equations

Algebra Level pending

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

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


The answer is 69.

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