JEE Mains · Maths · STD 12 - 1. relation and function
If the domain of the function \(f(x)=\log _e\) \(\left(\frac{2 x+3}{4 x^2+x-3}\right)+\cos ^{-1}\left(\frac{2 x-1}{x+2}\right)\) is \((\alpha, \beta]\), then the value of \(5 \beta-4 \alpha\) is equal to
- A \(10\)
- B \(12\)
- C \(11\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(\frac{2 x+3}{4 x^2+x-3}>0 \text { and }-1 \leq \frac{2 x-1}{x+2} \leq 1 \) \(\frac{2 \times+3}{(4 x-3)(x+1)}>0 \quad \frac{3 x+1}{x+2} \geq 0 \quad \& \quad \frac{x-3}{x+2} \leq 0 \) \((-\infty,-2) \cup\left[\frac{-1}{3}, \infty\right) \quad \ldots . .(1) \)…
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