If the domain of the function f(x)=sin^-1 ((1)/(x^2-2x-2) ) is (-infty,alpha]cup[beta,gamma]cup[delta,infty) , then alpha+beta+gamma+delta is equal to :

Functions: If the domain of the function f(x)=sin^-1 ((1)/(x^2-2x-2) ) is… | JEE Main 2026

JEE Main 2026 (Online) 24th January Evening ShiftQuestion 1

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

Functions

$2$$3$$4$✓ Correct answer$5$

Solution

Need $|x^2-2x-2|\ge1$: $x^2-2x-3\ge0$ gives $x\le-1$ or $x\ge3$; $x^2-2x-1\le0$ gives $1-\sqrt2\le x\le1+\sqrt2$. Sum $-1+(1-\sqrt2)+(1+\sqrt2)+3=4$.

Functions - JEE Mathematics question (JEE Main 2026 (Online) 24th January Evening Shift)

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