Given $R = {(x, y) : x, y \in W, x^{2} + y^{2} = 25}$ , where $W$ is the set of all whole numbers. Find the domain and range of $R$ .

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Solution

We have $3^{2} + 4^{2} = 25$ or, $4^{2} + 3^{2} = 25$ and $0^{2} + (5)^{2} = 25$ or, $5^{2} + 0^{2} = 25$ .
So the domain of $R$ is ${0, 3, 4, 5}$ . [ Values corresponding to $x$ for $x$ being whole number]
And the range is ${0, 3, 4, 5}$ . [ Values corresponding to $y$ for $y$ being whole number]

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