If the domain of the function f ( x ) = sin − 1 ( 2 x + 3 x − 1 ) is R − ( α , β ) , then 12 α β is equal to :

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If the domain of the function f ( x ) = sin − 1 ( 2 x + 3 x − 1 ​ ) is R − ( α , β ) , then 12 α β is equal to :

TestHub · Accepted Answer

Domain of f ( x ) = sin − 1 ( 2 x + 3 x − 1 ​ ) is ​ 2 x + 3  = 0& x  = 2 − 3 ​ and ​ 2 x + 3 ( x − 1 ) ​ ​ ≤ 1 ∣ x − 1∣ ≤ ∣2 x + 3∣ ​ ​ For ∣2 x + 3∣ ≥ ∣ x − 1∣ x ∈ ( − ∞ , − 4 ] ∪ ( − 3 2 ​ , ∞ ) α = − 4& β = − 3 2 ​ : 12 α β = 32 ​

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