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Suppose a function f(x) satisfies the fo...

Suppose a function f(x) satisfies the following conditions
`f (x+y) =(f(x) +f(y))/(f +f(x) f(y))' AA x , y in R and f '(0)=1`
Also `-1lt f (x) lt 1, AA x in R`
f(x) increases in the complete interval :

A

`(-oo, -1) uu (-1,0) uu (0,1) uu (1,oo)`

B

`(-oo, oo)`

C

`(-oo, 1)uu (-1, 0)`

D

`(0,1)uu (1,oo)`

Text Solution

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The correct Answer is:
B
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