If a function `f: R ->R` be such that `f(x-f(y)) = f(f(y) )+xf(y)+f(x) – InterviewSolution

1.	If a function `f: R ->R` be such that `f(x-f(y)) = f(f(y) )+xf(y)+f(x) -1 AA x , y in R` then `f(2)=`A. 1B. 3C. `-1`D. none of these
Answer» Correct Answer - C We have, `f(x-f(y))=f(f(y))+xy(dy)+f(x)-2" (1)"` Put `x=f(y)=0` Then `f(0)=f(0)+0+f(0)-1` `therefore" "f(0)=1` Putting `f(y)=x` `therefore" "f(0)=f(x)+x^(2)+f(x)-1` Hence, `f(x)=1-(x^(2))/(2)`

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