JEE Main 2024 (Online) 30th January Morning ShiftQuestion 1
If the domain of the function $f(x)=\cos^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log_e(3-x)\right\}^{-1}$ is $[-\alpha,\beta)-\{\gamma\}$, then $\alpha+\beta+\gamma$ is equal to :
Functions
Solution
$\left|\frac{2-|x|}4\right|\le1\Rightarrow|x|\le6$; $3-x>0$ and $\log_e(3-x)\ne0\Rightarrow x<3,\ x\ne2$. Domain $[-6,3)-\{2\}$, so $6+3+2=11$.