Q2 of 50 Page 28

For the given function F = { (1, 3), (2, 5), (4, 7), (5, 9), (3, 1) }, write the domain and range.

We know that for any two non-empty sets A and B. A function f from A to B may be defined as a rule that assigns each element of set A to tha of set B in a unique way (∀ x ∈ A and y ∈ B).


We denote y = f(x) which means mean y is a function of x. so the set A is called the domain of the function and set B is called the co-domain of the function. y is called as the image of x under f and x is called a preimage of y. Range may be defined as the set of all image and it’s a subset of co-domain.


We can represent the function in set as described below


f = {(a,b) / a ∈ A and b ∈ B}


Where A is the domain and B is the pre-domain.


So as per data given,


F = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}


Here


Domain = {1, 2, 3, 4, 5}


Range = {1, 3, 5, 7, 9}


More from this chapter

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9

In a village of 120 families, 93 families use firewood for cooking, 63 families use kerosene, 45 families use cooking gas, 45 families use firewood and kerosene, 24 families use kerosene and cooking gas, 27 families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.

 1

State whether each of the following arrow diagrams define a function or not. Justify your answer.

 3

Let A = { 10, 11, 12, 13, 14 }; B = { 0, 1, 2, 3, 5 } and fi : A → B , i = 1,2,3.

State the type of function for the following (give reason):


(i) f1 = { (10, 1), (11, 2), (12, 3), (13, 5), (14, 3) }


(ii) f2 = { (10, 1), (11, 1), (12, 1), (13, 1), (14, 1) }


(iii) f3 = { (10, 0), (11, 1), (12, 2), (13, 3), (14, 5) }

 4

If X = {1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine which of the following relations from X to Y are functions? Give reason for your answer. If it is a function, state its type.

(i) R1 = {(x, y)| y = x + 2, x ∈ X , y ∈ Y }


(ii) R2 = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}


(iii) R3 = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}


(iv) R4 = {(1, 3), (2, 5), (4, 7), (5, 9), (3, 1)}