Part of the domain of the function f (x) = √{cosx - (1 / 2)} / (6 + 35x - 6x^2) lying in the interval [-1, 6] is (1) [-1 / 6, π / 3] (2) [5π / 3, 6] (3) [-1 / 5, π / 3] ⋃ [5π / 3, 6] (4) (-1 / 6, π / 3] ⋃ [5π / 3, 6]

1) [-1 / 6, π / 3]

2) [5π / 3, 6]

3) [-1 / 5, π / 3] ⋃ [5π / 3, 6]

4) (-1 / 6, π / 3] ⋃ [5π / 3, 6]

Solution: (4)

f (x) = √{cosx – (1 / 2)} / (6 + 35x – 6x2)

cosx ≥ (1 / 2), (6 – x) (1 + 6x) > 0 or cosx ≤ (1 / 2), (6 – x) . (1 + 6x) < 0

x ∈ (-1 / 6, π / 3] ⋃ [5π / 3, 6]

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