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Reviewed CSCA Mathematics question · Hard

Consider the function f(x) = sqrt(2x + 6) / (x^2 - 3x - 4). What is the domain of f?

  1. [-3, -1) ∪ (-1, 4) ∪ (4, ∞)
  2. (-∞, -1) ∪ (-1, 4) ∪ (4, ∞)
  3. [-3, ∞)
  4. [-3, -1) ∪ (4, ∞)
Show the answer and explanation

Correct answer

A. [-3, -1) ∪ (-1, 4) ∪ (4, ∞)

Principle or equation

The domain of a function involving a square root requires the radicand to be nonnegative; the denominator must not be zero.

Why this answer is correct

Radicand: 2x + 6 ≥ 0 → x ≥ -3. Denominator: x^2 - 3x - 4 = (x - 4)(x + 1) ≠ 0 → x ≠ 4 and x ≠ -1. Combining: x ≥ -3, x ≠ -1, x ≠ 4. In interval notation: [-3, -1) ∪ (-1, 4) ∪ (4, ∞).

Example

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

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