Calculus
Domain of Inverse Trigonometric Functions
jee_main_2026_jan_21_shift_1
Grade None
Question:
If the domain of the function f(x) = cos⁻¹((2x-5)/(11-3x)) + sin⁻¹(2x² - 3x + 1) is [α, β], then α + 2β is equal to:
Step-by-Step Solution
Key Concept: Find domain of cos⁻¹(u): -1 ≤ u ≤ 1 and sin⁻¹(v): -1 ≤ v ≤ 1.
Step 1: For sin⁻¹(2x² - 3x + 1): -1 ≤ 2x² - 3x + 1 ≤ 1 => x(2x-3) ≤ 0 => x ∈ [0, 3/2]. Step 2: For cos⁻¹((2x-5)/(11-3x)): -1 ≤ (2x-5)/(11-3x) ≤ 1. Solving gives x ∈ [0, 3/2]. Step 3: Domain = [0, 3/2]. α = 0, β = 3/2. α + 2β = 3.
Correct Answer: B
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