If f(x) = 1/(1 − x) for x ≠ 1, then (f∘f∘f)(x) equals:
If f(x) = 1/(1 − x) for x ≠ 1, then (f∘f∘f)(x) equals:
- A. x
- B. 1/x
- C. 1/(1 − x)
- D. (x − 1)/x
Answer: A) x
Explanation: f(f(x)) = f(1/(1−x)) = 1/(1 − 1/(1−x)) = (1−x)/(1−x−1) = (1−x)/(−x) = (x−1)/x. Then f(f(f(x))) = f((x−1)/x) = 1/(1 − (x−1)/x) = 1/((x − x + 1)/x) = x. So (f∘f∘f)(x) = x.
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