Determine the domain and range of the following relation.R = {(a, b) /

1.	Determine the domain and range of the following relation.R = {(a, b) / b = \|a – 1\|, a ∈ Z, \|a\| < 3}
Answer» R = {(a, b) / b = \|a – 1\|, a ∈ Z, \|a\| < 3} Since a ∈ Z and \|a\| < 3, a < 3 and a > -3 ∴ -3 < a < 3 ∴ a = -2, -1, 0, 1, 2 b = \|a – 1\| When a = -2, b = 3 When a = -1, b = 2 When a = 0, b = 1 When a = 1, b = 0 When a = 2, b = 1 Domain (R) = {-2, -1, 0, 1, 2} Range (R) = {0, 1, 2, 3}

Determine the domain and range of the following relation.R = {(a, b) / b = |a – 1|, a ∈ Z, |a| < 3}

Answer»

R = {(a, b) / b = |a – 1|, a ∈ Z, |a| < 3}

Since a ∈ Z and |a| < 3, a < 3 and a > -3

∴ -3 < a < 3

∴ a = -2, -1, 0, 1, 2

b = |a – 1|

When a = -2, b = 3

When a = -1, b = 2

When a = 0, b = 1

When a = 1, b = 0

When a = 2, b = 1

Domain (R) = {-2, -1, 0, 1, 2}

Range (R) = {0, 1, 2, 3}