What is the domain of the function f(x) = sqrt(x + 2) / (x - 3)?

A x >= -2

B x != 3

C x >= -2 and x != 3

D x > -2 and x < 3

✓ Correct Answer: Option C

For the square root, x + 2 must be ≥ 0, so x ≥ -2. For the denominator, x - 3 cannot be 0, so x ≠ 3. Both conditions must be met.

💡 Why is C) the correct answer?

The correct answer to the question "What is the domain of the function f(x) = sqrt(x + 2) / (x - 3)?" is Option C: x >= -2 and x != 3.

The other options — A) x >= -2, B) x != 3, D) x > -2 and x < 3 — are incorrect for this CLEP Exam Prep question. As explained above: For the square root, x + 2 must be ≥ 0, so x ≥ -2. For the denominator, x - 3 cannot be 0, so x ≠ 3. Both conditions must be met.

📚 About This CLEP Exam Prep Practice Question

This 3-level CLEP Exam Prep question from the College Algebra topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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What is the domain of the function f(x) = sqrt(x + 2) / (x - 3)?

✓ Correct Answer: Option C

📚 About This CLEP Exam Prep Practice Question

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