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Relations and Functions

Short Answer Type

51.

Determine the domain and range of the relation defined as :

$space space space space space space space space space space space straight R space equals space left curly bracket left parenthesis straight x comma space straight y right parenthesis space colon space straight x element of straight N comma space straight y element of straight N comma space straight x less than 5 comma space straight y space equals space 3 straight x space plus space 1 right curly bracket$

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52.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by aRb = {(a, b) : a, $straight b element of straight A$ , a divide b}. determine its domain and range.

115 Views

53. Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function? If it is a function, determine the domain and range.

(i) {(2, 3), (2, 4), (2, 5)} (ii) {(2, 2), (3, 3), (4, 5), (5, 3)}

132 Views

54.

Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

(a) {(2,2), (3, 2), (4,2), (5,2)} (b) {(2, 3), (3,4),(4,5),(3,5)}

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55.

Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

{(2, 3), (2, 4), (2, 5)}

110 Views

56.

Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

{(2, 4), (3, 4), (4, 5)}

103 Views

57. Find the domain and range of the following functions :

space space space space space space space space space space space space space space space left parenthesis straight a right parenthesis space straight f left parenthesis straight x right parenthesis space equals space minus open vertical bar straight x close vertical bar space space space space space space

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58. Find the domain and range of the following functions :

$space space space space space space space space space straight f left parenthesis straight x right parenthesis space equals space square root of 4 minus straight x squared end root$

f(x) = $space space space space space space space space space square root of 4 minus straight x squared end root$

The function is not defined, when 4-x²is negative.

D_f= {x : 4 -x²_{$greater or equal than$ 0}}
D_f= {x : x² - 4 $less or equal than$ } = {x:(x-2)(x+2) $less or equal than$ 0}={x:x $space space element of$ [-2, 2]}

Hence, D_f= [-2, 2]

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Hence, R_f= All reals $space space space space space space space space greater or equal than 0 space space or space straight R subscript straight f equals left square bracket 0 comma space infinity right square bracket$