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Problem 12 - Entrance Test

If f(x) = x/(x-1), what is f(f(f(x)))?

Correct: C

f(x) = x/(x-1). f(f(x)) = f(x/(x-1)) = (x/(x-1)) / ((x/(x-1)) - 1) = (x/(x-1)) / ((x - (x-1))/(x-1)) = (x/(x-1)) / (1/(x-1)) = x. Therefore, f(f(f(x))) = f(x) = x/(x-1).