Let `f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0` and f(0)=0 – InterviewSolution

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1.	Let `f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0` and f(0)=0 then the value of `f(1) +f(2)=`A. `-1`B. 0C. 1D. none of these
Answer» Correct Answer - B `f(x+(1)/(y))+f(x-(1)/(y))=2f(x)f((1)/(y))AA x, y in R` Given f(0) = 0 Putting `x=0, y=(1)/(x)`, we get `f(x)+f(-x)=2f(0)f(x)` `rArr" "f(x)+f(-x)=0` `rArr" "f(x)=-f(-x)` Putting x = 1, y = -1, we get `rArr" "f(2)+f(0)=2[f(1)]^(2)` `rArr" "f(2)=2[f(1)]^(2)` Putting `x=-1, y=-1,` we get `rArr" "f(-2)=2f(-1)f(-1)` `rArr" "-f(2)=2(f(1))^(2)` `rArr" "f(2)=-f(2)` `rArr" "f(2)=0` `rArr" "f(1)=0` `therefore" "f(1)=f(2)=0` `therefore" "f(1)+f(2)=0`

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