QJEEM22Ma07d4: JEE Main 2022 Mathematics - Class 12 JEEM22Ma07d4 Solution: The domain of the function f ( x ) = sin − 1 ⁡ ( x 2 − 3 x + 2…

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

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)

Step-by-Step Verified Solution