If R₁ = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R₁.

Given: R₁ = {(x, y) | y = 2x + 7, where x ∈R and – 5 ≤ x ≤ 5} is a relation

To find: the domain and Range of R₁

Explanation: Given R₁ = {(x, y) | y = 2x + 7, where x ∈R and – 5 ≤ x ≤ 5}

Now we need to find the domain and range of set R₁.

So, the domain of R₁ consists of all the first elements of all the ordered pairs of R₁, i.e., x, and it is also given – 5 ≤ x ≤ 5, so

Domain of R₁ = [-5, 5]

And the range of R contains all the second elements of all the ordered pairs of R₁, i.e., y and it is also given so

y = 2x + 7

Now x ∈ [-5,5]

Multiply both sides with 2, we get

So 2x∈[-10, 10]

Add both sides with 7, we get

2x + 7∈[-3, 17]

Or, y∈[-3, 17]

So,

Range of R₁ = [-3, 17]