If A = { - 2 , - 1 , 1 , 2 } and f = x , 1 x : x ∈ A . List the domain of f .

A relation f is defined by f : x → 1 x i.e, f x = 1 x , where x ∈ { - 2 , - 1 , 1 , 2 } Now, When x = - 2 , f - 2 = - 1 2 , so - 2 , - 1 2 When x = - 1 , f - 1 = - 1 , so - 1 , - 1 When x = 1 , f 1 = 1 , so 1 , 1 When x = 2 , f 2 = 1 2 , so 2 , 1 2 Hence, the roster form is - 2 , - 1 2 , - 1 , - 1 , 1 , 1 , , 2 , 1 2 . ∴ The domain of f is - 2 , - 1 , 1 , 2 . (Set of all first elements in ordered pairs)

If A = { - 2 , - 1 , 1 , 2 } and f = x , 1 x : x ∈ A . List the range of f .

A relation f is defined by f : x → 1 x i.e, f x = 1 x , where x ∈ { - 2 , - 1 , 1 , 2 } Now, When x = - 2 , f - 2 = - 1 2 , so - 2 , - 1 2 When x = - 1 , f - 1 = - 1 , so - 1 , - 1 When x = 1 , f 1 = 1 , so 1 , 1 When x = 2 , f 2 = 1 2 , so 2 , 1 2 Hence, the roster form is - 2 , - 1 2 , - 1 , - 1 , 1 , 1 , , 2 , 1 2 . ∴ The range of f is - 1 2 , - 1 , 1 , 1 2 . (Set of all second elements in ordered pairs)

If A = { - 2 , - 1 , 1 , 2 } and f = x , 1 x : x ∈ A . Is f a function ? Justify answer.

A relation f is defined by f : x → 1 x i.e, f x = 1 x , where x ∈ { - 2 , - 1 , 1 , 2 } Now, When x = - 2 , f - 2 = - 1 2 , so - 2 , - 1 2 When x = - 1 , f - 1 = - 1 , so - 1 , - 1 When x = 1 , f 1 = 1 , so 1 , 1 When x = 2 , f 2 = 1 2 , so 2 , 1 2 Hence, the roster form is - 2 , - 1 2 , - 1 , - 1 , 1 , 1 , , 2 , 1 2 . By observing all the ordered pairs we can conclude that every element of x has a unique image. Therefore, the relation is a function.

E M B I B E

Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 6

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11th ICSE

IMPORTANT

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Does the following arrow diagram represent a function $?$ Justify your answer.

Important Questions on Relations and Functions

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11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 6

Does the following arrow diagram represent a function $?$ Justify your answer.

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11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 7

Does the adjacent arrow diagram represent a function $?$ If so, write its range.

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11th ICSE

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Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 8

The adjacent arrow diagram represents a relation. Represent the relation in the roster form. Is this relation a function $?$ Give reasons for your answer.

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11th ICSE

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Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 9

The adjacent arrow diagram represents a relation. List the pairs that satisfy the relation. Is this relation a function $?$ Also find the rule(relation) for the above correspondence.

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Understanding ISC Mathematics Class 11 Volume 1>Chapter 2 - Relations and Functions>EXERCISE 2.3>Q 10

Write the relation represented by the adjoining diagram, by listing the ordered pairs. State the domain, the co-domain and the range of the relation. Is the relation a function $?$

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