Which of the following functions is an odd function?

A f(x) = x² + 1

B f(x) = |x|

C f(x) = x³ - x

D f(x) = x³ + x²

✓ Correct Answer: Option C

A function is odd if f(-x) = -f(x). For f(x) = x³ - x, f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x). Options A and B are even, D is neither.

💡 Why is C) the correct answer?

The correct answer to the question "Which of the following functions is an odd function?" is Option C: f(x) = x³ - x.

The other options — A) f(x) = x² + 1, B) f(x) = |x|, D) f(x) = x³ + x² — are incorrect for this CLEP Exam Prep question. As explained above: A function is odd if f(-x) = -f(x). For f(x) = x³ - x, f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x). Options A and B are even, D is neither.

📚 About This CLEP Exam Prep Practice Question

This 2-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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Which of the following functions is an odd function?

✓ Correct Answer: Option C

📚 About This CLEP Exam Prep Practice Question

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