JEE Mains · Maths · STD 12 - 1. relation and function
If the domain of the function \(f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)\) is \([\alpha, \beta) \cup(\gamma, \delta]\), then \(|3 \alpha+10(\beta+\gamma)+21 \delta|\) is equal to \(.......\).
- A \(23\)
- B \(22\)
- C \(24\)
- D \(21\)
Answer & Solution
Correct Answer
(C) \(24\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sec ^{-1} \frac{2 x}{5 x+3}\) \(\left|\frac{2 x}{5 x+3}\right|\) \(\left|\frac{2 x}{5 x+3}\right| \geq 1 \Rightarrow|2 x| \geq|5 x+3|\) \((2 x)^2-(5 x+3)^2 \geq|5 x+3|\) \((7 x+3)(-3 x-3) \geq 0\) \(\frac{-\quad-\quad-}{-1} \quad-\frac{3}{7}\)…
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