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in Sets, relations and functions by (53.1k points)
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The domain of the function f(x) = sin-1(3 - x)/In(|x| - 2) is

(A)  [2, 4]

(B)  (2, 3) ∪ (3, 4]

(C)  [2, ∞) 

(D)  (−∞ ,−3)∪{2,∞)

1 Answer

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Best answer

Correct option  (B) (2, 3) ∪ (3, 4]

Explanation :

We have

Let us consider

g(x) = sin-1 (3 - x) ⇒ −1 ≤ 3 - x ≤  1

 The domain of g (x ) is [2, 4] and let us consider

 Therefore, the domain of f(x) is

(2 ,4] { − 3} = (2 ,3) (3,4]

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