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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)` isA. `[0,infty)`B. `{0,1}`C. `R`D. `{0}` |
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Answer» Correct Answer - 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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