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]
Create a free account to view solution
View Solution FreeMore Function Questions
A function f : R → R satisfies the condition x2 f(x) + f(1 - x) = 2x - x4. Then f(x) is:...f(x) = is -...If f(x) is a polynomial function satisfying the condition f(x). f(1/x) = f(x) + f(1/x) and f(2) = 9 then-...If f(x) = loge(x + ), then f−1(x) equals-...The range of the function f(x) = log√2 (2 - log2(16 sin2x + 1)) is...