If domain of function f(x)=sin ^{-1}left(frac{x-1}{2 x+3}right) is R-(α, β) then 12 α β is equal

English

Gujarati

Hindi

1.Relation and Function

hard

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 :

A

$36$

B

$24$

C

$40$

D

$32$

(JEE MAIN-2024)

Solution

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

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

$Image$

$ \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$

Standard 12

Mathematics

Share

Similar Questions

The period of the function $f (x) =$$\frac{{|\sin x| + |\cos x|}}{{|\sin x – \cos x|}}$ is

normal

If $\,\,f(x) = \left\{ {\begin{array}{*{20}{c}}
{3 + x;\,\,\,\,\,x \geqslant 0} \\
{2 – 3x;\,\,\,\,\,x < 0}
\end{array}} \right.$ then $\mathop {\lim }\limits_{x \to 0} f(f(x))$ is equal to –

normal

Let $S=\{1,2,3,4,5,6\}$. Then the number of oneone functions $f: S \rightarrow P(S)$, where $P(S)$ denote the power set of $S$, such that $f(n) \subset f(m)$ where $n < m$ is $………………$

hard

(JEE MAIN-2023)

If $f:R \to R$ satisfies $f(x + y) = f(x) + f(y)$, for all $x,\;y \in R$ and $f(1) = 7$, then $\sum\limits_{r = 1}^n {f(r)} $ is

medium

(AIEEE-2003)

Let for $a \ne {a_1} \ne 0,$ $f\left( x \right) = a{x^2} + bx + c\;,g\left( x \right) = {a_1}{x^2} + {b_1}x + {c_1},p\left( x \right) = f\left( x \right) – g\left( x \right),$ If $p\left( x \right) = 0$ only for $ x=-1 $ and $p\left( { – 2} \right) = 2$ then value of $p\left( 2 \right)$ is

hard

(AIEEE-2011)