Class 12 Inverse Trigonometric Functions · Short Answer2 Marksdomains_and_ranges
Class 12 Maths · Inverse Trigonometric Functions · Short Answer #54
State the real domain and principal range of \(f(x)=\tan^{-1}x\).
✅ Step-by-Step Solution
Final Answer: Domain R; range (−π/2,π/2).
- Tangent restricted to (−π/2,π/2) is continuous, strictly increasing and maps onto R.
- Its inverse therefore accepts every real input and returns exactly one angle in that open interval; the endpoints are never attained.
- Hence the domain is R and the principal range is (−π/2,π/2).
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Tangent restricted to (−π/2,π/2) is continuous, strictly increasing and maps onto R.
- [1 mark] Its inverse therefore accepts every real input and returns exactly one angle in that open interval; the endpoints are never attained.
- [0.5 marks] Hence the domain is R and the principal range is (−π/2,π/2).
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