1.

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Answer»

`1-X^(2013)`
`sqrt(|x|)+1`
`(pi)/(2tan^(-1)|x|)`
`(2)/(1+k" In "|x|)`

SOLUTION :`(f((1)/(x))-1)=(1)/((f(x)-1))i.e., (f((1)/(x))-1)`
is reciprocal of `(f(x)-1).`
Now, for `f(x)=((pi)/(2))/(tan^(-1)|x|)`
`f(x)-1=(cot^(-1)|x|)/(tan^(-1)|x|),f((1)/(x))-1=(tan^(-1)|x|)/(cot^(-1)|x|)`
ALSO for `f(x)=(2)/(1+k" In " |x|)`
`f(x)-1=(1-k" In " |x|)/(1+k" In " |x|),f((1)/(x))-1=(1+k" In "|x|)/(1-k " In "|x|)`


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