Let `f(x)`be real valued and differentiable function on `R`such that ` – InterviewSolution

InterviewSolution

1.	Let `f(x)`be real valued and differentiable function on `R`such that `f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y))``f(0)`is equalsa. b. c. d. none of theseA. odd functionB. even functionC. odd and even function simultaneouslyD. neither even nor odd
Answer» Correct Answer - A Putting x = y= 0, we get `f(0)=(f(0)+f(0))/(1-[f(0)]^(2))` `rArr" "f(0)[f^(2)(0)+1]=0rArr f(0)=0( "since "f^(2)(0) ne-1).` Now putting `y=-x`, we get `f(0)=(f(x)+f(-x))/(1-f(x).f(-x))` `rArr" "f(x)+f(-x)=0` `rArr" "f(-x)=-f(x)rArr f(x)` is an odd function.

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