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BALTIC-WAY 1995 Problem 10

  • Answer

Find all real-valued functions ff defined on the set of all non-zero real numbers such that:

(i) f(1)=1f(1)=1,

(ii) f(1x+y)=f(1x)+f(1y)f\left(\frac{1}{x+y}\right)=f\left(\frac{1}{x}\right)+f\left(\frac{1}{y}\right) for all non-zero x,y,x+yx, y, x+y,

(iii) (x+y)f(x+y)=xyf(x)f(y)(x+y) f(x+y)=x y f(x) f(y) for all non-zero x,y,x+yx, y, x+y.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=\frac{1}{x}

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