Functional Equation 2

Algebra Level pending

Consider a function f : R + → R + f: \mathbb R^+ \to \mathbb R^+ satisfying f ( y f ( x y ) ) = x 4 f ( y ) f\left(y f\left( \dfrac xy \right)\right) =\dfrac{x^4}{f(y)} . What is f ( 1111 ) f(1111) ?


The answer is 1234321.

Rezwan Arefin by Rezwan Arefin , 19, Bangladesh

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1 solution

Barr Shiv
Dec 11, 2018

plug in y=1 you get: f(f(x))=x^4/f(1) let's aussme f(1)=1. therefore f(f(x))=x^4. a function that setisfies it is f(x)=x^2 if one plugs it the equation holds therefore. f(1111)=1111^2=1234321

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