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JEE Main 20249 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2024 · 9 April · Morning Shift · Mathematics · Functions

If the domain of the function f(x)= ^ -1 ((x-1)/(2 x+3)) is R-(α,...

If the domain of the function f(x)=sin⁡−1f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)isis\mathbf{R}-(\alpha, \beta),then, then12 \alpha \beta is equal to :If the domain of the function f(x)= ^ -1 ((x-1)/(2 x+3)) is R-(α, β) , then 12 α β is equal to :

Options

  1. A32
  2. B40
  3. C24
  4. D36

Correct answer

A. 32

Step-by-step solution

Domain of f(x)=sin⁡−1f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)isis2x+3≠0x≠−32 and ∣(x−1)2x+3∣≤1∣x−1∣≤∣2x+3∣\begin{aligned} & 2 x+3 \neq 0 & x \neq \frac{-3}{2} \text{ and }\left|\frac{(x-1)}{2 x+3}\right| \leq 1 \\ & |x-1| \leq|2 x+3| \end{aligned}<img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/OkE4iMeQTtMyxIVV_CzlE2otwc_q_uu2dNbLNcCRc8E.original.fullsize.png"><br /> For ∣2x+3∣≥∣x−1∣x∈(−∞,−4]∪(−23,∞)α=−4β=−23:12αβ=32\begin{aligned} & \text{ 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\end{aligned}$
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