The domain of the function $f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$ is :
Solution
$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$
<br/><br/>$-1 \leq \frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1$
<br/><br/>$$
\begin{aligned}
& \frac{x^{2}-3 x+2}{x^{2}+2 x+7} \leq 1 \\\\
& x^{2}-3 x+2 \leq x^{2}+2 x+7 \\\\
& 5 x \geq-5 \\\\
& x \geq-1
\end{aligned}
$$
<br/><br/>And $\frac{x^{2}-3 x+2}{x^{2}+2 x+7} \geq-1$
<br/><br/>$x^{2}-3 x+2 \geq-x^{2}-2 x-7$
<br/><br/>$2 x^{2}-x+9 \geq 0$
<br/><br/>$x \in R$
<br/><br/>(i) $\cap$ (ii)
<br/><br/>Domain $\in[-1, \infty)$
About this question
Subject: Mathematics · Chapter: Inverse Trigonometric Functions · Topic: Domain and Range
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