# If R =

Question:

If R = {(xy) : xy ∈ Z, x2 + y2 = 25}, then Domain (R) = .................... and Range (R) = __________.

Solution:

If R = { (xy) : xy ∈ 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 $(R)=\{0,3,4,5\}$