Discussion

Question:

If f(x) = $\frac{x + 1}{x - 1}$ , x ≠ 1, find f¹⁰⁰(2). Here, fⁿ(x) = $f (f (\dots n t i m e s (x)))$ .

Explanation:

f(2) = $\frac{2 + 1}{2 - 1}$ = 3

f²(2) = f(f(2)) = f(3) = $\frac{3 + 1}{3 - 1}$ = 2

f³(2) = f(f(f(2))) = f(f(3)) = f(2) = $\frac{2 + 1}{2 - 1}$ = 3

f⁴(2) = f(f(f(f(2)))) = f(3) = $\frac{3 + 1}{3 - 1}$ = 2

f⁵(2) = f(f(f(f(f(2))))) = f(2) = $\frac{2 + 1}{2 - 1}$ = 3

∴ f¹⁰⁰(2) = f²(2) = 2

Hence, option (a).

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