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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

The function f(x) = √(x - 4) is continuous on which of the following sets?

The function f(x) = √(x - 4) requires x - 4 ≥ 0 for the square root to be defined in real numbers. Therefore, the domain (and continuity set) is [4, ∞), where x is greater than or equal to 4.

  1. A(-∞, 4]
  2. B[4, ∞)Correct
  3. C(-∞, ∞)
  4. D(-∞, 4) ∪ (4, ∞)

Explanation

For f(x) = √(x - 4) to be defined and continuous, the expression under the square root must be non-negative: x - 4 ≥ 0, which means x ≥ 4. The domain is [4, ∞). Since f is a square root function (which is continuous wherever defined), f is continuous on its entire domain [4, ∞). The set (-∞, 4] includes points where f is undefined, so it is incorrect.

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