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Reviewed CSCA Mathematics question · Standard

What is the domain of the function f(x) = sqrt(4 - x) / (x^2 - 5x + 6)?

  1. (-∞, 4] except x = 2 and x = 3
  2. (-∞, 4]
  3. [4, ∞) except x = 2 and x = 3
  4. (-∞, 4) except x = 2
Show the answer and explanation

Correct answer

A. (-∞, 4] except x = 2 and x = 3

Principle or equation

Domain: radicand ≥ 0 and denominator ≠ 0.

Why this answer is correct

Radicand: 4 - x ≥ 0 → x ≤ 4. Denominator: x^2 - 5x + 6 = (x-2)(x-3) ≠ 0 → x ≠ 2,3. Combine: (-∞, 4] excluding 2 and 3.

Example

For sqrt(1-x)/(x-1), domain: x ≤ 1 and x ≠ 1 → (-∞, 1).

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