let $f(x)$ be a real valued function defined for all positive x, satisfying $f(x+y)=f(xy)$ for all positive x, y. Prove that f is a constant function.

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let $f(x)$ be a real valued function defined for all positive x, satisfying $f(x+y)=f(xy)$ for all positive x, y. Prove that f is a constant function.

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