If f(x) = x/(x − 1), x ≠ 1, then f(f(f(x))) equals: A. x B. 1/x C. −x D. x/(x − 1) Answer: D) x/(x − 1) Explanation: f(f(x)) = f(x/(x−1)) = (x/(x−1))/((x/(x−1))−1) = x. So f is its own inverse, thus f³(x) = f(f²(x)) = f(x) = x/(x−1).

imo class 12 relations and functions

If f(x) = x/(x − 1), x ≠ 1, then f(f(f(x))) equals:

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If f(x) = x/(x − 1), x ≠ 1, then f(f(f(x))) equals:

Answer: D) x/(x − 1)

Explanation: f(f(x)) = f(x/(x−1)) = (x/(x−1))/((x/(x−1))−1) = x. So f is its own inverse, thus f³(x) = f(f²(x)) = f(x) = x/(x−1).