If the domain of the function f(x)=fraccos^-1sqrtx^2-x+1sqrtsin^-1 ((2x-1)/(2) ) is the interval (alpha,beta] , then alpha+beta is equal to :

Functions: If the domain of the function f(x)=fraccos^-1sqrtx^2-x+1sqrtsin^-1… | JEE Main 2021

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 1

If the domain of the function $f(x)=\frac{\cos^{-1}\sqrt{x^{2}-x+1}}{\sqrt{\sin^{-1}\left(\frac{2x-1}{2}\right)}}$ is the interval $(\alpha,\beta]$, then $\alpha+\beta$ is equal to :

Functions

$1$$2$$\frac{1}{2}$$\frac{3}{2}$✓ Correct answer

Solution

$\cos^{-1}$ needs $x^2-x+1\le1$: $0\le x\le1$. Denominator needs $0<\frac{2x-1}2\le1$: $\frac12<x\le\frac32$. Domain $(\frac12,1]$, so $\alpha+\beta=\frac32$.

Functions - JEE Mathematics question (JEE Main 2021 (Online) 22nd July Evening Shift)

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