Let `f(x)=(1)/(1-x)."Then (fp (fof)) (x)"`A. x for all ` xin R`B. x fo – InterviewSolution

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1.	Let `f(x)=(1)/(1-x)."Then (fp (fof)) (x)"`A. x for all ` xin R`B. x for all `x in R-[1]`C. x for all `x imn R-[0,1]`D. None of these
Answer» Correct Answer - C We have, `f(x)=(1)/(1-x)` Clearly, f(x) is defined for all `x ne 1`. For any `x(ne 1)` we have `"fof" (x)=f(f (x))=f((1)/(1-x))=(1)/((1-(1)/(1-x)))=(x-1)/(x)` It is evident from the defination of `f of (x)` is defined for all `x ne 0,1`. `[fo (fof)](x)=f(fof(x))=f((x-1)/(x))=(1)/((1-(x-1)/(x)))=x` `"Hence", [fo(fof)(x)=x" for all " x in R[(0,1)]`

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