Let A = {5, 6, 7, 8 }; B = { –11, 4, 7, –10,–7, –9,–13 } and f = {( x,y) : y = 3 - 2x, x ∈ A, y ∈ B }|

(i) Write down the elements of f. (ii) What is the co-domain?

(iii) What is the range? (iv) Identify the type of function.

Here we are given

A = {5, 6, 7, 8 }

B = {–11, 4, 7, –10,–7, –9,–13 }

f = {( x,y) : y = 3 - 2x, x A, y B }

so we can find

f = {( x,y) : y = 3 - 2x, x A, y B }

f(5) = 3- 2×5 = 3-10 = -7

f(6) = 3 – 2×6 = 3-12 = -9

f(7) = 3 – 2×7 = 3-14 = -11

f(8) = 3 – 2×8 = 3- 16 = -13

(i) the elements of f are

From the above expression we get that

f = {(5,-7),(6,-9),(7,-11),(8,-13)}

(ii) co-domain

The co-domain is B and it can be given as

Codomain B = {-11,4, 7,-10,-7,-9,-13}

(iii) Range

Range may be defined as the image of A in B present in the function.

Range of f = {-7,-9,-11,-13}

(iv) type of function

From the above data and the diagram it’s clear that the given function is a one-one function as all the element A has a unique and single image in B. it’s not a onto function as the range is not same as the co-domain .