$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$ $-1 \leq \frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1$ $\begin{aligned} & \frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1 \\\\ & x^{2}-3 x+2 \leq x^{2}+2 x+7 \\\\ & 5 x \geq-5 \\\\ & x \geq-1 \end{aligned}$ And $\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \geq-1$ $x^{2}-3 x+2 \geq-x^{2}-2 x-7$ $2 x^{2}-x+9 \geq 0$ $x \in R$ (i) $\cap$ (ii) Domain $\in[-1, \infty)$