Sets, Relations and Function: If R=\(x,y):x,yinmathbfZ,x^2+3y^2le8\ is a relation on the set of… | JEE Main 2020

JEE Main 2020 (Online) 2nd September Morning ShiftQuestion 1

If $R=\{(x,y):x,y\in\mathbf{Z},x^2+3y^2\le8\}$ is a relation on the set of integers $\mathbf{Z}$, then the domain of $R^{-1}$ is :

Sets, Relations and Function

$\{-2,-1,0,1,2\}$$\{-2,-1,1,2\}$$\{-1,0,1\}$✓ Correct answer$\{0,1\}$

Solution

Domain of $R^{-1}$ = range of $R$ = set of $y\in\mathbf Z$ for which some integer $x$ satisfies $x^2+3y^2\le8$ ($x=0$ works when possible). Need $3y^2\le8\Rightarrow y^2\le2$, so $y\in\{-1,0,1\}$. Option (C).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2020 (Online) 2nd September Morning Shift)

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