Question
If $$R = \left\{ {\left( {x,\,y} \right):x,\,y\, \in \,I{\text{ and }}{x^2} + {y^2} \leqslant 4} \right\}$$ is a relation in $$I,$$ the domain of $$R$$ is :
A.
$$\left\{ {0,\,1,\,2} \right\}$$
B.
$$\left\{ { - 2,\, - 1,\,0} \right\}$$
C.
$$\left\{ { - 2,\, - 1,\,0,\,1,\,2} \right\}$$
D.
$$I$$
Answer :
$$\left\{ { - 2,\, - 1,\,0,\,1,\,2} \right\}$$
Solution :
$${x^2} + {y^2} \leqslant 4,$$ represents all points interior to the circle $${x^2} + {y^2} = 4,$$ hence $$ - 2 \leqslant x \leqslant 2$$ and $$ - 2 \leqslant y \leqslant 2$$
$$\therefore $$ integral values of $$x$$ are $$ - 2,\, - 1,\,0,\,1,\,2$$