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Question
Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.
Solution
When x = 1
y = 7 ∈ N
So (1, 7) ∈ R.
Again for x = 2.
y = `2 + 6/2`
= 2 + 3
= 5 ∈ N
So (2, 5) ∈ R.
Again for x = 3
y = `3 + 6/3`
= 3 + 2
= 5 ∈ N
(3, 5) ∈ R.
Similarly for x = 4
y = `4 + 6/4` ∉ N and for x= 5
y = `5 + 6/5` ∉ N
Thus R = {(1, 7), (2, 5), (3, 5)}
Where Domain of R = {1, 2, 3}
Range of R = {7, 5}
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