JEE MAIN - Mathematics (2020 - 2nd September Morning Slot - No. 16)
If R = {(x, y) : x, y
$$ \in $$ Z, x2 + 3y2
$$ \le $$ 8} is a relation
on the set of integers Z, then the domain of R–1 is :
{0, 1}
{–2, –1, 1, 2}
{–1, 0, 1}
{–2, –1, 0, 1, 2}
Explanation
Given R = {(x, y) : x, y
$$ \in $$ Z, x2 + 3y2
$$ \le $$ 8}
So R = {(0,1), (0,–1), (1,0), (–1,0), (1,1), (1,-1)
(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}
$$ \Rightarrow $$ R : { -2, -1, 0, 1, 2} $$ \to $$ {-1, 0, 1}
$$ \therefore $$ R-1 : {-1, 0, 1} $$ \to $$ { -2, -1, 0, 1, 2}
$$ \therefore $$ Domain of R–1 = {-1, 0, 1}
So R = {(0,1), (0,–1), (1,0), (–1,0), (1,1), (1,-1)
(-1,1), (-1,-1), (2,0), (-2,0), (-2,0), (2,1), (2,-1), (-2,1), (-2,-1)}
$$ \Rightarrow $$ R : { -2, -1, 0, 1, 2} $$ \to $$ {-1, 0, 1}
$$ \therefore $$ R-1 : {-1, 0, 1} $$ \to $$ { -2, -1, 0, 1, 2}
$$ \therefore $$ Domain of R–1 = {-1, 0, 1}
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