Let f(x) = x –(1/3) and A denote the area of the region bounded by f(x) and the X-axis, when x varies from –1 to 1. Which of the following statements is/are True?
1. f is continuous in [–1, 1] 2. f is not bounded in [–1, 1] 3. A is nonzero and finite
(A) 2 only
(B) 3 only
(C) 2 and 3 only
(D) 1, 2 and 3
Answer: (C)
Explanation: 1 is false: function is not a Continuous function. As a change of 1 in x leads to ∞ change in f(x). For example when x is changed from -1 to 0. At x = 0, f(x) is ∞ and at x = 1, f(x) is finite.
2 is True: f(x) is not a bounded function as it becomes ∞ at x = 0.
3 is true: A denote the area of the region bounded by f(x) and the X-axis. This area is bounded, we can calculate it by doing integrating the function [See this]
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