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.

Question

Philoid · Accepted 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