 Hello and welcome to the session. In this session we discuss the following question which says let r equal to x goes to 2x square plus 1 where x belongs to the set containing the elements 0, 1, 2, 3. List the elements of r is r a mapping. Find the domain and range of mapping. Before we move on to the solution, let's discuss some points related to the mapping. Consider a and b to be two non-empty sets when we say mapping from a to b is a rule which associates every element of set a to a unique element of set b. If an element a of set a is associated with a unique element of set b, then b is called the image of a under the mapping. Also the elements of set a from the domain of the mapping set of images in set b from the range of the mapping. This is the key idea to be used in this question. Let's proceed with the solution now. We have r is equal to x which goes to 2x square plus 1 and we have this x belongs to the set containing the elements 0, 1, 2, 3. Let set a be equal to the set containing the elements 0, 1, 2, and 3. And we obtain the elements of set b by putting the values of x as 0, 1, 2, and 3 in 2x square plus 1. So for x equal to 0 we have 2 into 0 plus 1 that is 1. So first element would be 1 for x equal to 1 we have 2 into 1 square plus 1 that is equal to 2 plus 1 which is 3. So second element is 3. Now for x equal to 2 in this we have 2 into 2 square is 4 plus 1 that is equal to 8 plus 1 which is 9. So 9 is the third element of set b. Now for x equal to 3 we have 2 into 3 square that is 9 plus 1. 9 twos are 18 plus 1 which is 19. So 19 is the fourth element of set b. Now first we are supposed to list the elements of r. So r is the set of ordered pairs in which the first component would be the elements from set a and the second component would be the elements from set b. So first ordered pair formed would be 0, 1 where 0 is from the set a and 1 is from the set b and would satisfy this relation. The second ordered pair would be 1, 3 where 1 is from the set a, 3 is from the set b and they satisfy this relation. Then the next ordered pair formed would be 2, 9 in which 2 is from set a and 9 is from set b and they also satisfy this relation. Then the last ordered pair formed would be 3, 19 in which we have taken 3 from set a and 19 from set b and they also satisfy this relation r. So we have listed the elements of r. Now next we are supposed to find out is r a mapping. Now for r to be a mapping we have that every element of set a is associated to a unique element of set b. So we can say that r is a mapping because every element of set a is associated with a unique element of set b. Now next we are supposed to find the domain and range of the mapping. In the key idea we have that the elements of set a they form the domain of the mapping and the set of images in set b they form the range of the mapping. Now what is an image? We know that if an element a of set a is associated with a unique element b of set b then this b is called the image of the element a of set a under the mapping. So we have the domain of the mapping is the set a that is set a is the set containing the elements 0, 1, 2, 3. Thus we have domain of the mapping is the set containing the elements 0, 1, 2 and 3. Now we will find out the set of images in set b so that we get the range of the mapping. As we know that every element of set a is associated with a unique element of set b so we get the set of images in set b as the set containing the elements 1, 3, 9, 19. And so we have the range of the mapping is the set of the images in set b which is the set containing the elements 1, 3, 9, 19. So we get the range of the mapping as this set. So this completes the session. Hope you have understood the solution of this question.