Question

Is R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} relation a function. Give reasons. If it is a function determine its domain and range​

Answer 1

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

It is a function as every input has a single 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.