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NCERT Class XI Mathematics - Relations and Functions - Solutions
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Question : 20 of 36
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Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, 3), (1, 5), (2, 5)}.
Solution:
(i) We have a relation R = {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} Since 2, 5, 8, 11, 14, 17 are the elements of domain of R having their unique images. ∴ The given relation is a function. Hence domain = {2, 5, 8, 11, 14, 17} and Range = {1}. (ii) We have a relation R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} Since 2, 4, 6, 8, 10, 12, 14 are the elements of domain of R having their unique images. ∴ The given relation is a function. Hence domain = {2, 4, 6, 8, 10, 12, 14} and Range = {1, 2, 3, 4, 5, 6, 7}. (iii) We have a relation R = {(1, 3), (1, 5), (2, 5)} Since the distinct ordered pairs (1, 3) and (1, 5) have same first element i.e., 1 does not have a unique image under R. ∴ It is not a function.
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