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Question

Let $f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\} $. If ${f^{n + 1}}(x) = f({f^n}(x))$ for all n $\in$ N, then ${f^6}(6) + {f^7}(7)$ is equal to :

${7 \over 6}$
$ - {3 \over 2}$
${7 \over {12}}$
$ - {{11} \over {12}}$

Solution

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