JEE Mains · Maths · STD 12 - 1. relation and function
If the domain of the function \(f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)\) is \(R-(\alpha, \beta)\) then \(12 \alpha \beta\) is equal to :
- A \(36\)
- B \(24\)
- C \(40\)
- D \(32\)
Answer & Solution
Correct Answer
(D) \(32\)
Step-by-step Solution
Detailed explanation
Domain of \(f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)\) is \( 2 x+3 \neq 0\ \&\ x \neq \frac{-3}{2} \text { and }\left|\frac{(x-1)}{2 x+3}\right| \leq 1 \) \(|x-1| \leq|2 x+3|\) \( \text { For }|2 x+3| \geq|x-1| \)…
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