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JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1
Let f(x)=x−1x+1,   x∈R−{0,−1,1}.f(x) = \frac{{x - 1}}{{x + 1}},\,\,\,x \in {\text{R}} - \left\{ {0, - 1,1} \right\}. If fn+1(x)=f(fn(x)){f^{n + 1}}\left( x \right) = f\left( {{f^n}\left( x \right)} \right) for all n∈N,n \in N, then f6(6)+f7(7){f^6}\left( 6 \right) + {f^7}\left( 7 \right) is equal to:
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Correct option: B
−32- \frac{3}{2}
Option B (−32- \frac{3}{2}) is correct because after finding the pattern of the function composition, we can simplify the expression f6(6)+f7(7){f^6}(6) + {f^7}(7) to f2(6)+f3(7){f^2}(6) + {f^3}(7), which evaluates to −32- \frac{3}{2}.

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