JEE Main 2026 (Online) 21st January Morning ShiftQuestion 1
If the domain of the function $f(x)=\cos^{-1}\left(\frac{2x-5}{11-3x}\right)+\sin^{-1}\left(2x^2-3x+1\right)$ is the interval $[\alpha,\beta]$, then $\alpha+2\beta$ is equal to :
Inverse Trigonometric Functions
Solution
$|2x^2-3x+1|\le1\Rightarrow0\le x\le\frac32$. On this interval $11-3x>0$ and $|2x-5|\le11-3x$ always holds. Domain $[0,\frac32]$, so $\alpha+2\beta=3$.