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all right thanks for watching and today i would like to answer a really cool question i found on stack exchange namely find all the continuous function f such that f of x y equals y f of x plus x f of y so itamp;#39;s kind of like a prada loo for functions and again just to emphasize here we just assume f is continuous and x and y are positive just to make things easier otherwise replace it by absolute values that should be fine and the way we do this we simply take this equation and weamp;#39;ll transform it into one thatamp;#39;s more familiar in particular consider the following ingenious trick letamp;#39;s divide this by x y so x y and x y then what we get we get that f of x y over x y equals so this y cancels out and you get f of x over x and f of y over y in particular define this to be g of x okay so g of x is f of x over x then what we get we get that g of x y equals g of x plus g of y but this is actually a identity which i covered in another video and in that video we fou
