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 :-

Question

Aicharya · Accepted Answer

$\begin{aligned} & \log _3\left(\log _7\left(8-\log _2\left(\mathrm{x}^2+4 \mathrm{x}+5ight)ight)ight) \gt 0 \ & \log _2\left(\mathrm{x}^2+4 \mathrm{x}+5ight) \lt 1 \ & \mathrm{x}^2+4 \mathrm{x}+3 \lt 0 \ & \Rightarrow \mathrm{x} \in(-3,-1) \ & -1 \leq \frac{7 \mathrm{x}+10}{\mathrm{x}-2} \leq 1 \ & \Rightarrow \mathrm{x} \in[-2,-1] \ & \alpha=-3, \beta=-1, \gamma=-2, \delta=-1 \ & \alpha^2+\beta^2+\gamma^2+\delta^2=15 \ & 	ext { option }(1)\end{aligned}$

Let the domains of the functions $\mathrm{f}(\mathrm{x})=\log _4 \log _3 \log _7\left(8-\log…

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