JEE Mains · Maths · STD 11- 2. Relation and Function
Let the domains of the functions
\(\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right)\right)\) and \(g(x)=\sin ^{-1}\left(\frac{7 x+10}{x-2}\right)\) be \((\alpha, \beta)\) and \([\gamma, \delta]\), respectively. Then \(\alpha^2+\beta^2+\gamma^2+\delta^2\) is equal to :-
- A \(15\)
- B \(13\)
- C \(16\)
- D \(14\)
Answer & Solution
Correct Answer
(A) \(15\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \log _3\left(\log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right)\right)\right) \gt 0 \\ & \log _2\left(\mathrm{x}^2+4 \mathrm{x}+5\right) \lt 1 \\ & \mathrm{x}^2+4 \mathrm{x}+3 \lt 0 \\ & \Rightarrow \mathrm{x} \in(-3,-1) \\ & -1 \leq \frac{7…
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