If f(x) = (x + 1)/(x − 1) for x ≠ 1, then f(f(f(3))) equals:

First compute f(f(x)). f(f(x)) = [(x+1)/(x−1) + 1] / [(x+1)/(x−1) − 1] = [2x/(x−1)] / [2/(x−1)] = x.

So f is its own inverse, and f(f(f(3))) = f(3) = 4/2 = 2.

Direct check: f(3) = 2, f(2) = 3, f(3) = 2. ✓

Tip: any f(x) = (ax + b)/(cx − a) satisfies f(f(x)) = x. When f is its own inverse, an odd number of applications collapses to a single f.