If satisfies f(x-f(y))=f(f(y))+x f(y)+f(x)-1

MATHEMATICS · Subjective · AoPS · Mathematics · Functions · Functions

Problem

If f:R→Rf:\mathbb{R}\to\mathbb{R} satisfies f(x−f(y))=f(f(y))+xf(y)+f(x)−1, for all x,y∈R,f(x-f(y))=f(f(y))+x f(y)+f(x)-1,\text{ for all }x,y\in\mathbb{R}, then −f(10)7\frac{-f(10)}{7} is ……………\dots\dots\dots\dots\dots

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