FunctionHard
Question
The domain of definition of f(x) = sin-1 (|x - 1| - 2) is:
Options
A.[- 2, 0] ∪[2, 4]
B.(- 2, 0) ∪ (2, 4)
C.[- 2, 0] ∪ [1, 3]
D.(- 2, 0) ∪ (1, 3)
Solution
f(x) = sin-1 (|x - 1| - 2)
For domain - 1 ≤ |x - 1| - 2 ≤ 1
⇒ 1 ≤ |x - 1| ≤ 3 ⇒ x - 1 ∈ [-3, -1] ∪ [1, 3]
⇒ x ∈ [-2, 0] ∪ [2, 4]
For domain - 1 ≤ |x - 1| - 2 ≤ 1
⇒ 1 ≤ |x - 1| ≤ 3 ⇒ x - 1 ∈ [-3, -1] ∪ [1, 3]
⇒ x ∈ [-2, 0] ∪ [2, 4]
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