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📝 Continuity of Inverse Functions

📖 From Calculus • 2. Limits and Continuity an Introduction • 25 questions available

Practice MCQs for Continuity of Inverse Functions. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

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📝 Sample Questions

Q1. Theorem 1.6.2 states that if \(f\) is one-to-one and continuous, then \(f^{-1}\) is:

🔹 A. Continuous on its domain

🔹 B. Discontinuous on its domain

🔹 C. Differentiable on its domain

🔹 D. Bounded on its domain

💡 Difficulty: easy | ✅ Correct: A

Q2. Why does the continuity of \(f\) imply the continuity of \(f^{-1}\) geometrically?

🔹 A. Because reflection about \(y=x\) preserves continuity

🔹 B. Because reflection preserves differentiability

🔹 C. Because inverse functions are always continuous

🔹 D. Because reflection flips the graph

💡 Difficulty: medium | ✅ Correct: A

Q3. What is the range of \(\sec^{-1} x\)?

🔹 A. \((-\infty,\infty)\)

🔹 B. \([-1,1]\)

🔹 C. \([0,\pi]\) except \(\pi/2\)

🔹 D. \((0,\infty)\)

💡 Difficulty: hard | ✅ Correct: C

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Trigonometric Functions

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