Q. 95.0( 2 Votes )

Let A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}. Let f = {(x, y) : x ϵ A, y ϵ B and y = 2x – 1}. Write f in roster form. Show that f is a function from A to B. Find the domain and range of f.

Answer :

Given: A = {2, 3, 5, 7} and B = {3, 5, 9, 13, 15}

f = {(x, y): x A, y B and y = 2x – 1}


For x = 2


y = 2x – 1


y = 2(2) – 1


y = 3 B


For x = 3


y = 2x – 1


y = 2(3) – 1


y = 5 B


For x = 5


y = 2x – 1


y = 2(5) – 1


y = 9 B


For x = 7


y = 2x – 1


y = 2(7) – 1


y = 13 B


f = {(2, 3), (3, 5), (5, 9), (7, 13)}


Now, we have to show that f is a function from A to B


Function:


(i) all elements of the first set are associated with the elements of the second set.


(ii) An element of the first set has a unique image in the second set.


f = {(2, 3), (3, 5), (5, 9), (7, 13)}



Here, (i) all elements of set A are associated with an element in set B.


(ii) an element of set A is associated with a unique element in set B.


f is a function.


Dom (f) = 2, 3, 5, 7


Range (f) = 3, 5, 9, 13


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