A) \[R=\{(0,3),(0,-3),(3,0),(-3,0)\}\]
B) Domain of \[R=\{-3,0,3\}\]
C) Range of \[R=\{-3,0,3\}\]
D) None of these
Correct Answer: D
Solution :
| [d] \[{{x}^{2}}+{{y}^{2}}=9\Rightarrow {{y}^{2}}=9-{{x}^{2}}\] |
| \[\Rightarrow y=\pm \sqrt{9-{{x}^{2}}}\] |
| \[x=0\Rightarrow y=\pm \sqrt{9-0}=\pm 3\in Z\] |
| \[x=\pm 1\Rightarrow y=\pm \sqrt{9-1}=\pm \sqrt{8}\notin Z\] |
| \[x=\pm 2\Rightarrow y=\pm \sqrt{9-4}=\pm \sqrt{5}\notin Z\] |
| \[x=\pm 3\Rightarrow y=\pm \sqrt{9-9}=0\in Z\] |
| \[x=\pm 4\Rightarrow y=\pm \sqrt{9-16}=\pm \sqrt{-7}\notin Z\] And so on, |
| \[\therefore R=\{(0,3),(0,-3),(3,0),(-3,0)\}\] |
| Domain of \[R=\{x:(x,y)\in R\}=\{0,3,-3\}\] |
| Range of \[R=\{y:(x,y)\in R\}=\{3,-3,0\}.\] |
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