A function `f: R -> R` satisfy the equation `f (x)f(y) - f (xy)= x+y` – InterviewSolution

1.	A function `f: R -> R` satisfy the equation `f (x)f(y) - f (xy)= x+y` for all `x, y in R` and `f(y) > 0`, thenA. `f(x)f^(-1)(x)=x^(2)-4`B. `f(x)f^(-1)(x)=x^(2)-6`C. `f(x)f^(-1)(x)=x^(2)-1`D. none of these
Answer» Correct Answer - C Taking x = y = 1, we get `f(1)f(1)-f(1)=2` `rArr" "f^(2)(1)-f(1)-2=0` `rArr" "(f(1)-2)(f(1)+1)=0` `rArr" "f(1)=2` Taking y = 1, we get `f(x).f(1)-f(x)=x+1` `rArr" "f(x)=x+1` `rArr" "f^(-1)(x)=x-1` `therefore" "f(x).f^(-1)(x)=x^(2)-1`

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