Consider the function f(x) = sqrt(9 - x^2) / (x - 4). Which of the following is the domain of f?
Show the answer and explanation
Correct answer
A. [-3, 3]
Principle or equation
Domain: radicand ≥ 0 and denominator ≠ 0. For sqrt(9 - x^2), need 9 - x^2 ≥ 0 => -3 ≤ x ≤ 3. Denominator x - 4 ≠ 0 => x ≠ 4. Since 4 is not in [-3,3], domain is [-3,3].
Why this answer is correct
9 - x^2 ≥ 0 gives x ∈ [-3, 3]. x - 4 = 0 at x = 4, which is outside this interval, so no additional exclusion. Thus domain is [-3, 3].
Example
For f(x) = sqrt(4 - x^2)/(x - 5), domain is [-2, 2] because 5 is outside.
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