The range of f(x) = 2 sin⁻¹x + 3 cos⁻¹x is:
The range of f(x) = 2 sin⁻¹x + 3 cos⁻¹x is:
- A. [π/2, 5π/2]
- B. [0, 2π]
- C. [π, 2π]
- D. [0, π]
Answer: C) [π, 2π]
Explanation: sin⁻¹x + cos⁻¹x = π/2. So f(x) = 2 sin⁻¹x + 3(π/2 − sin⁻¹x) = 3π/2 − sin⁻¹x. As sin⁻¹x ∈ [−π/2, π/2], f(x) ∈ [3π/2 − π/2, 3π/2 + π/2] = [π, 2π].
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