Let `f(x)=(alphax)/((x+1)),x!=-1.`The for what value of `alpha`is `f(f – InterviewSolution

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1.	Let `f(x)=(alphax)/((x+1)),x!=-1.`The for what value of `alpha`is `f(f(x))=x ?``sqrt(2)`(b) `-sqrt(2)`(c) `1`(d) `-1`A. `sqrt2`B. `-sqrt2`C. 1D. `-1`
Answer» Correct Answer - D We have `f(f(x))=x " " "for all "x ne -1` `Rightarrow f((alpha x)/(x+1))=x "for all "xne -1` `Rightarrow (alpha((alpha x)/(x+1)))/((alpha x)/(x+1)+1)=x" for all"xne-1` `Rightarrow (alpha^(2)x)/(alphax+x+1)=x"for all"x ne-1` `Rightarrow alpha^(2)x=(alpha+1)x^(2)+x"for all "x ne-1` `Rightarrow (alpha+1)x^(2)+(1-alpha^(2))x=0"for all "xne-1` `Rightarrow alpha+1=0 and 1-alpha^(2)=0` `Rightarrow alpha=-1`

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