If the domain of the function f(x)=sin -1 (x-1/2 x+3 ) is R-(α, β) then 12 α β is equal to :

Mathematics · Inverse Trigonometric Functions

JEE Main 2024 — 9 April, Shift 1 — Question 11

If the domain of the function $f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)$ is $R-(\alpha, \beta)$ then $12 \alpha \beta$ is equal to :

Domain of $f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)$ is

$2 x+3 \neq 0 \& x \neq \frac{-3}{2}$ and $\left|\frac{(x-1)}{2 x+3}\right| \leq 1$

$|x-1| \leq|2 x+3|$

For $|2 x+3| \geq|x-1|$

$x \in(-\infty,-4] \cup\left(-\frac{2}{3}, \infty\right)$

$\alpha=-4 \& \beta=-\frac{2}{3}: 12 \alpha \beta=32$

Answer key and solution verified before publishing.

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