Let `f(x)=(alpha x)/(x+1), x ne -1.` Then, for what value of `alpha " – InterviewSolution

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1.	Let `f(x)=(alpha x)/(x+1), x ne -1.` Then, for what value of `alpha " is " f[f(x)]=x` ?A. `sqrt(2)`B. `-sqrt(2)`C. 1D. -1
Answer» Correct Answer - D Given, `f(x)=(alphax)/(x+1)` `f[f(x)]=f((alphax)/(x+1))=(alpha((alphax)/(x+1)))/((alphax)/(x+1)+1)` `=((alpha^(2)x)/(x+1))/((alphax+(x+1))/(x+1))=(alpha^(2)x)/((alpha+1)x+1)=x` [given] ...(i) `rArr alpha^(2)x=(alpha +1)x^(2)+x` `rArr x[alpha^(2)-(alpha +1)x-1]=0` `rArr x(alpha +1)(alpha -1-x)=0` `rArr alpha -1=0 and alpha +1=0` `rArr alpha = -1` But `alpha =1` does nto satisfy the Eq. (i).

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