Suppose that f(x) is a continuous function on the interval [a, b] and g(x) is a function such that g(x) = f(x) for all x ∈ [a, b]. Which of the following statements is true about the function h(x) = g(x) + f(x)?

Core Concept

This question tests the student's understanding of continuity and the properties of continuous functions. Since g(x) and f(x) are both continuous, their sum h(x) is also continuous. Option B is incorrect because h(x) may not be differentiable. Option C is incorrect because h(x) does not have a discontinuity at x = a. Option D is incorrect because h(x) does not have a discontinuity at x = b.