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Reviewed CSCA Mathematics question · Standard

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

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

Correct answer

A. (-∞, 3] except x = 2

Principle or equation

The domain consists of all real numbers for which the expression is defined: the radicand must be nonnegative and the denominator must not be zero.

Why this answer is correct

Radicand: 6 - 2x ≥ 0 → x ≤ 3. Denominator: x^2 - 5x + 6 = (x-2)(x-3) ≠ 0 → x ≠ 2,3. Since x=3 is already excluded by x ≤ 3, the domain is (-∞,3] except x=2.

Example

For f(x) = sqrt(x-1)/(x-2), domain is [1,2) ∪ (2,∞).

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