Class 9 Advanced Maths Chapter 3 Relations and Functions Ex 3.3 Solutions

Students often refer to NCERT Class 9 Advanced Maths Solutions Chapter 3 Relations and Functions Ex 3.3 to verify their answers.

Advanced Maths Class 9 Exercise 3.3 Solutions

Class 9 Advanced Maths Ex 3.3 Solutions

Question 1.
Which of the following relations are functions? Justify your answer.

Solution:
Core Rule for Functions:
A relation is a function if every domain element maps to exactly one codomain element.
(a) Function
Justification: Every domain element maps to exactly one output.
Mappings: 2 → 0, – 1 → 0, -2 → 0, 3 → 1.

(b) Not a Function
Justification: Element -1 has no corresponding output value.
Reason: Every input must map to an output.

(c) Function
Justification: Every input maps to exactly one output value.
Mappings: 1 → 1, 1.2 → 1, 1.3 → 1, 1.9 → 1, 2.5 → 2.

(d) Not a Function
Justification: Element 5 maps to three different outputs.
Outputs for 5: Maps to 7, 5 and 2.

Question 2.
Which of the following relations from A = {3, 5, 7, 9} to B = {1, 2, 3, 4, 5} are functions from A to B?
(a) R₁ = {(3, 2), (5, 4), (7, 5), (9, 5)}
(b) R₂ = {(1, 3), (3, 5), (5, 7)}
(c) R₃ = {(2, 3), (2, 5), (2, 7), (3, 5), (3, 7), (5, 7)}
(d) R₄ = {(3, 3), (5, 5)}
Solution:
(a) R₁ = {(3, 2), (5, 4), (7, 5), (9, 5)}
Check elements of A:

1. 3 has one image 2
2. 5 has one image 4
3. 7 has one image 5
4. 9 has one image 5

Every element of A has exactly one image.
R₁ is a function.

(b) R₂ = {(1, 3), (3, 5), (5, 7)}
Here:

1. 1 ∉ A
2. 7 ∉ B
3. element 9 ∈ A has no image

So, this is not a function from A to B.
R₂ is not a function.

(c) R₃ = {(2, 3), (2, 5), (2, 7), (3, 5), (3, 7), (5, 7)}
Here,

1. 2 ∉ A
2. 7 ∉ B
3. One element has multiple images

Hence, not a function from A to B.
R₃ is not a function.

(d) R₄ = {(3, 3), (5, 5)}
Elements 7 and 9 of A have no images.
So it is not a function.
R₄ is not a function.
Hence, only R₁ is a function from A to B.