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Let f(x) = x/(x - 1). Then the 19-fold composition (f ∘ f ∘... ∘ f)(x) is equal to:

1. x/(x - 1)
2. (x/(x - 1))¹⁹
3. 19x/(x - 1)
4. x

Correct answer: x/(x - 1)

Solution

f(f(x)) = (x/(x-1))/((x/(x-1))-1) = x, so f composed with itself is the identity. Since 19 is odd, the 19-fold composition equals f(x) = x/(x-1).

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