Let f(x) and g(x) be two functions such that g(x) = x - 1/x and f∘g(x) = x³ - 1/x³. What is g[f(x) - 3x] equal to?

We have f(g(x)) = x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x) = g(x)³ + 3g(x). So f(t) = t³ + 3t. Therefore f(x) = x³ + 3x, and f(x) - 3x = x³. Now g[f(x) - 3x] = g(x³) = x³ - 1/x³. Wait, that gives option (a). Let me recheck: g(t) = t - 1/t, so g(x³) = x³ - 1/x³. Hmm. But if we interpret differently: actually g(x³) = x³ - 1/x³, which is option (a). The correct answer is (a).