FunctionHard
Question
The function f(x) = cot-1 
+ cos-1 
is defined on the set S, where S is equal to:
+ cos-1 is defined on the set S, where S is equal to:Options
A.{0, 3}
B. (0, 3)
C.{0, - 3}
D.[- 3, 0]
Solution
f(x) = cot-1 
+ cos-1 
for domain
x(x + 3) ≥ 0 and 0 ≤ x2 + 3x + 1 ≤ 1
⇒ x ∈ (-∞, -3] ∪ [0, ∞) and x2 + 3x + 1 ≥ 0 and x2 + 3x ≤ 0 ⇒x ∈ [-3, 0]
Taking intersection
x ∈ {-3, 0}
+ cos-1 for domain
x(x + 3) ≥ 0 and 0 ≤ x2 + 3x + 1 ≤ 1
⇒ x ∈ (-∞, -3] ∪ [0, ∞) and x2 + 3x + 1 ≥ 0 and x2 + 3x ≤ 0 ⇒x ∈ [-3, 0]
Taking intersection
x ∈ {-3, 0}
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