JEE Main 2023 (Online) 15th April Morning ShiftQuestion 1
If the domain of the function $f(x)=\log_e\left(4x^{2}+11x+6\right)+\sin^{-1}(4x+3)+\cos^{-1}\left(\frac{10x+6}{3}\right)$ is $(\alpha,\beta]$, then $36|\alpha+\beta|$ is equal to
Functions
Solution
$4x^2+11x+6>0\Rightarrow x<-2$ or $x>-\frac34$; $-1\le x\le-\frac12$; $-\frac{9}{10}\le x\le-\frac3{10}$. Domain $\left(-\frac34,-\frac12\right]$, so $36\cdot\frac54=45$.