Consider the function f(x) = {1/x if x ≠ 0, x if x = 0}. Which of the following statements is true about the function f(x) on the interval [-1, 1]?

Core Concept

The primary reason this is true is that the function f(x) meets the three conditions for continuity at x = 0: it is defined at x = 0, the limit exists, and the limit equals the value of the function at x = 0. The function is continuous on [0, 1] because it is continuous at x = 0 and there are no other points of discontinuity in the interval. Options A and C are incorrect because the function is not continuous at x = 0; option D is incorrect because the function is continuous at x = 0.