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If f:RtoR is a function which satisfies ...

If `f:RtoR` is a function which satisfies the condition `f(x)+f(y)=f((x+y)/(1+xy))` for all `x, y in R` except `xy=-1`, then range of `f(x)` is

A

`[0,infty)`

B

`{0,1}`

C

`R`

D

`{0}`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(1)+f(1)=f(1)impliesf(1)=0`
`f(x)+f(1)=f((1+x)/(1+x))=f(1)` for `x ne-1`
`impliesf(x)=0` for all `x ne -1`
also `f(-1)+f(-1)=f(-1)impliesf(-1)=0`
`thereforef(x)=0` for all `x ne R`
`thereforef(x)` is odd as well as even function.
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