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Problem 8 - Olympiad

Let f(x) = (x^2 - 1) / (x - 1) for x ≠ 1. If f is to be made continuous at x = 1, what value must be assigned to f(1)?

Correct: C

For x ≠ 1, f(x) = (x^2 - 1) / (x - 1) = (x - 1)(x + 1) / (x - 1) = x + 1. The limit as x → 1 is lim_(x→1) (x + 1) = 2. To make f continuous at x = 1, we must define f(1) = 2. The correct answer is C.