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

Question:

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.

Solution:

According to the question,

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

The domain of R1 consists of all the first elements of all the ordered pairs of R1, i.e., x,

It is also given – 5 ≤ x ≤ 5.

Therefore,

Domain of R1 = [–5, 5]

The range of R contains all the second elements of all the ordered pairs of R1, i.e., y

It is also given y = 2x + 7

Now x ∈ [–5,5]

Multiply LHS and RHS by 2,

We get,

2x ∈ [–10, 10]

Adding LHS and RHS with 7,

We get,

2x + 7 ∈ [–3, 17]

Or, y ∈ [–3, 17]

So,

Range of R1 = [–3, 17]

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