Question

If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.

Answer 1

R = {(x, y) : x, y ∈ W, 2x + y = 8}

$$\begin{gathered} \mathrm{As}\mathrm{y}=8-2\mathrm{x} \\ \mathrm{For}\mathrm{x}=0,\mathrm{y}=8 \\ \mathrm{For}\mathrm{x}=1,\mathrm{y}=6 \\ \mathrm{For}\mathrm{x}=2,\mathrm{y}=4 \\ \mathrm{For}\mathrm{x}=3,\mathrm{y}=2 \\ \mathrm{For}\mathrm{x}=4,\mathrm{y}=0 \\ \mathrm{For}\mathrm{x}=5,\mathrm{y}<0 \\ \mathrm{So},\mathrm{y}<0\mathrm{for}\mathrm{all}\mathrm{x}>5 \end{gathered}$$

∴ Domain (R) = {0,1,2,3,4} and Range (R) = {0,2,4,6,8}