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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
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 L.H.S and R.H.S by 2
We get,
2x ∈ [–10, 10]
Adding L.H.S and R.H.S with 7
We get,
2x + 7 ∈ [–3, 17]
Or, y ∈ [–3, 17]
So,
Range of R1 = [–3, 17]
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