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Question
If x ≠ 1 and \[f\left( x \right) = \frac{x + 1}{x - 1}\] is a real function, then f(f(f(2))) is
Options
(a) 1
(b) 2
(c) 3
(d) 4
Solution
(c) 3 \[f\left( x \right) = \frac{x + 1}{x - 1}\] \[f(f(f(2))) \]
\[ = f\left( f\left( \frac{2 + 1}{2 - 1} \right) \right)\]
\[ = f\left( f(3) \right)\]
\[ = f\left( \frac{3 + 1}{3 - 1} \right)\]
\[ = f(2) = 3\]
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