Consider the piecewise function f(x) = {1/x if x ≠ 0, x² if x = 0}. Which of the following statements is true about the function f(x)?

Core Concept

The primary reason this is true is that the piecewise function has different definitions for x ≠ 0 and x = 0. The function f(x) is discontinuous at x = 0 because the value of the function approaches different values depending on the approach. Option A is incorrect because the function does not actually reach the value 1/x at x = 0; option C is incorrect because the limit exists; option D is incorrect because the function approaches different values depending on the approach.