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Let f(x) be real valued and differentiab...

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 equals a. b. c. d. none of these

A

odd function

B

even function

C

odd and even function simultaneously

D

neither even nor odd

Text Solution

Verified by Experts

The correct Answer is:
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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