Q5 of 50 Page 28

If R = {(a, - 2), (- 5, b), (8, c), (d, - 1)} represents the identity function, find the values of a, b, c and d.

a = - 2, b = -5, c = 8, d = - 1


Let’ consider that the identity function R be defined as A → A.


The identity function can be diagrammatically represented as,



From the diagram it’s clear that in case of identity function every element is related to itself


So a = -2, b = -5, c = 8 and d = -1


More from this chapter

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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)}

 6

A = {–2, –1, 1, 2 } and . Write down the range of f. Is f a function from A to A?

 7

Let f = {(2, 7), (3, 4), (7, 9), (–1, 6), (0, 2), (5, 3) } be a function from A = { –1, 0, 2, 3, 5, 7 } to B = { 2, 3, 4, 6, 7, 9}.