Question

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

Answer 1

QUESTION:
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.

Function :
Let A and B be any two non empty sets. A function f from A to B is a rule of correspondence that assigns each element x∈A to a unique element y∈B.
We denote y = f(x) to mean y is a function of x.

•Onto function : A function is said to be an onto function if every element in B has preimage in A.
Co domain = Range

•Range : The set of all the second elements of the ordered pairs of a relation is called the range of the relation.

SOLUTION :
f(x) = 3-2x (gx)
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 : f ={5, - 7) ,(6,-9), (7, - 11), (8 ,- 13)

ii)
Co - domain = {- 11, 4, 7, - 10 ,- 7, - 9, - 13}
iii) Range = {-7,-9,-11,-13}

PART IV IN THE ATTACHMENT..

HOPE THIS WILL HELP YOU...

Answer 2

It is given that ,

A = { 5 ,6 , 7 , 8 }

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

And

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

_____________________

x | y = 3 - 2x

____________________

5 | y = 3 - 2×5 = 3 - 10 = -7

____________________

6 | y = 3 - 2×6 = 3 - 12 = -9

____________________

7 | y = 3 - 2×7 = 3 - 14 = -11

____________________

8 | y = 3 - 2×8 = 3 - 16 = -13

____________________

Therefore ,

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

ii ) co-domain = B

iii ) Range = { -7 , - 9 , -11, -13 }

iv ) f is " into function ".

[ The function f : A -> B is such

that the range of function is subset

of co-domain , then the the

function is called into function ]

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