If `f(x)=log_(e)((1-x)/(1+x)),|x| lt 1, " then " f((2x)/(1+x^(2)))` is – InterviewSolution

InterviewSolution

1.	If `f(x)=log_(e)((1-x)/(1+x)),\|x\| lt 1, " then " f((2x)/(1+x^(2)))` is equal toA. `2f(x)`B. `2f(x^(2))`C. `(f(x))^(2)`D. `-2f(x)`
Answer» Correct Answer - A Given, `f(x)-log_(e)((1-x)/(1+x)),\|x\| lt 1,` then `f((2x)/(1+x^(2)))=log_(e)((1-(2x)/(1+x^(2)))/(1+(2x)/(1+x^(2)))) " "[ because \|(2x)/(1+x^(2))\| lt 1]` `=log_(e)(((1+x^(2)-2x)/(1+x^(2)))/((1+x^(2)+2x)/(1+x^(2))))=log_(e)(((1-x)^(2))/((1+x)^(2)))=log_(e)((1-x)/(1+x))^(2)` `=2 log_(e)((1-x)/(1+x)) " " [ because log_(e)\|A\|^(m)=m log_(e)\|A\|]` `=2f(x) " " [ because f(x)=log_(e)((1-x)/(1+x))]`

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