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.

If ( a , 8 ) and ( 2 , b ) are ordered pairs which belong to the mapping f : x → 3 x + 4 , where x ∈ R , find a and b .

Given function, f : x → 3 x + 4 , x ∈ R ∴ f x = 3 x + 4 → 1 Since, the ordered pairs a , 8 and 2 , b belongs to the given function ∴ f a = 8 ⇒ 3 a + 4 = 8 From 1 ⇒ a = 4 3 And f 2 = b ⇒ 6 + 4 = b From 1 ⇒ b = 10 Hence, a = 4 3 , b = 10 .

If a function f from R to R is defined by f = { ( x , 3 x - 5 ) : x ∈ R } , find the values of a and b given that ( a , 4 ) and ( 1 , b ) belong to f .

Given function f from R to R is defined by f = { ( x , 3 x - 5 ) : x ∈ R } ∴ f x = 3 x - 5 → 1 Since, the ordered pairs a , 4 and 1 , b belongs to the given function ∴ f a = 4 ⇒ 3 a - 5 = 4 From 1 ⇒ a = 3 And f 1 = b ⇒ 3 - 5 = b From 1 ⇒ b = - 2 Hence, a = 3 , b = - 2 .

E M B I B E

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

EASY

11th ICSE

IMPORTANT

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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.

Important Questions on Relations and Functions

EASY

11th ICSE

IMPORTANT

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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