For the function f(x) = sqrt(x - 3) / (x - 5), which of the following represents its domain?

A x ≥ 3

B x > 3 and x ≠ 5

C x ≥ 3 and x ≠ 5

D x > 5

✓ Correct Answer: Option C

For the square root to be defined, x - 3 ≥ 0, so x ≥ 3. For the denominator not to be zero, x - 5 ≠ 0, so x ≠ 5. Combining these conditions gives x ≥ 3 and x ≠ 5.

💡 Why is C) the correct answer?

The correct answer to the question "For the function f(x) = sqrt(x - 3) / (x - 5), which of the following represents its domain?" is Option C: x ≥ 3 and x ≠ 5.

The other options — A) x ≥ 3, B) x > 3 and x ≠ 5, D) x > 5 — are incorrect for this GRE Exam Prep question. As explained above: For the square root to be defined, x - 3 ≥ 0, so x ≥ 3. For the denominator not to be zero, x - 5 ≠ 0, so x ≠ 5. Combining these conditions gives x ≥ 3 and x ≠ 5.

📚 About This GRE Exam Prep Practice Question

This 3-level GRE Exam Prep question from the Quantitative Reasoning 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 GRE Exam Prep practice test or use flashcards for spaced repetition review.

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For the function f(x) = sqrt(x - 3) / (x - 5), which of the following represents its domain?

✓ Correct Answer: Option C

📚 About This GRE Exam Prep Practice Question

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