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  4. The domain of the function f(x)= sin -1((x2-3 x+2/x2+2 x+7)) is :

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Q. The domain of the function $f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)$ is :

JEE MainJEE Main 2022Inverse Trigonometric Functions

Solution:

$f(x)=\sin ^{-1}\left(\frac{x^2-3 x+2}{x^2+2 x+7}\right)$
Domain $\frac{x^2-3 x+2}{x^2+2 x+7} \geq-1$
and $\frac{x^2-3 x+2}{x^2+2 x+7} \leq 1$
$2 x^2-x+9 \geq 0$
and $5 x \geq-5 \Rightarrow x \geq-1$ $x \in R$
Hence Domain $x \in[-1, \infty)$