Question:
If R = {(x, y) : x, y ∈ Z, x2 + y2 = 25}, then Domain (R) = .................... and Range (R) = __________.
Solution:
If R = { (x, y) : x, y ∈ Z , x2 + y2 = 25}
Since x2 + y2 =25
$\therefore$ only possibilities for $x$ are $0,3,4$ and 5 and similarly for $y$ are $0,3,4$ and 5
i.e R = {(0, 5) , (3, 4) , (4, 3), (5, 0)}
$\left\{\because\right.$ all above satisfy $\left.x^{2}+y^{2}=25\right\}$
$\therefore$ Domain $(R)=\{0,3,4,5\}$ and Range $(R)=\{0,3,4,5\}$
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