JEE Mains · Maths · STD 12 - 1. relation and function
If the domain of the function \(f(x)=\log _e\left(4 x^2+11 x+6\right)+\sin ^{-1}\) \((4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right) \text { is }(\alpha, \beta]\) Then \(36|\alpha+\beta|\) is equal to :
- A \(63\)
- B \(45\)
- C \(72\)
- D \(54\)
Answer & Solution
Correct Answer
(B) \(45\)
Step-by-step Solution
Detailed explanation
\(f(x)=\ln \left(4 x^2+11 x+6\right)+\sin ^{-1}(4 x+3)\) \(+\cos ^{-1}\left(\frac{10 x+6}{3}\right)\) \(\text { (i) } 4 x^2+11 x+6 > 0\) \(4 x^2+8 x+3 x+6 > 0\) \((4 x+3)(x+2) > 0\) \(x \in(-\infty,-2) \cup\left(-\frac{3}{4}, \infty\right)\) \(\text { (ii) } 4 x+3 \in[-1,1]\)…
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