Question

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)}.​

Answer 1

Step-by-step explanation:

(i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)}

It is a function as every input has a single output.

output.

So, 2,5,8,11,14 and 17 are the elements of the domain of the given relation.

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)}

It is a function as every input has a single output.

So, 2,4,6,8,10,12 and 14 are the elements of the domain of the given

relation.

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 element 1 corresponds to two different images i.e., 3 and 5 . So, this relation is not a function.