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.
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