NCERT Class XI Mathematics - Relations and Functions - Solutions
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Question : 11
Total: 36
Let A = {1, 2, 3,......,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0,
where x, y ∈ A}. Write down its domain, codomain and range.
where x, y ∈ A}. Write down its domain, codomain and range.
Solution:
We have A = {1, 2, 3,........., 14}
Given relation R = {(x, y) : 3x – y = 0, where x, y ∈ A}
= {(x, y) : y = 3x, where x, y ∈ A} = {(x, 3x), where x, 3x ∈ A}
= {(1, 3), (2, 6), (3, 9), (4, 12)}
[Since 1 ≤ 3x ≤ 14 , ∴ 1/3 ≤ x ≤ 14/3 ⇒ x = 1 , 2 , 3 , 4]
Domain of R = {1, 2, 3, 4}
Codomain of R = {1, 2, ......., 14}
Range of R = {3, 6, 9, 12}.
Given relation R = {(x, y) : 3x – y = 0, where x, y ∈ A}
= {(x, y) : y = 3x, where x, y ∈ A} = {(x, 3x), where x, 3x ∈ A}
= {(1, 3), (2, 6), (3, 9), (4, 12)}
[Since 1 ≤ 3x ≤ 14 , ∴ 1/3 ≤ x ≤ 14/3 ⇒ x = 1 , 2 , 3 , 4]
Domain of R = {1, 2, 3, 4}
Codomain of R = {1, 2, ......., 14}
Range of R = {3, 6, 9, 12}.
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