Sarthaks Test
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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)}

1 Answer

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by (2.5k points)
 
Best answer
(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Since 2, 5, 8, 11, 14, and 17 are the elements of the domain of the given
relation having their unique images, this relation is a function. Here,
domain = {2, 5, 8, 11, 14, 17} and range = {1}
(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Since 2, 4, 6, 8, 10, 12, and 14 are the elements of the domain of the given
relation having their unique images, this relation is a function.
Here, domain = {2, 4, 6, 8, 10, 12, 14} and range = {1, 2, 3, 4, 5, 6, 7}
(iii) {(1, 3), (1, 5), (2, 5)}
Since the same first element i.e., 1 corresponds to two different images
i.e., 3 and 5, this relation is not a function.

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