Relation and Functions Lecture 3
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Part - 1

NCERT EXERCISE 2.3

Question 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i). {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii). {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii). {(1,3), (1,5), (2,5)}.

Question 3. A function f is defined by f(x)=2x – 5. Write down the values of
(i). f(0)
(ii). f(7)
(iii). f(-3)

Question 4. The function ‘t’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t(C)=\frac{9C}{5}+32
(i). t(0)
(ii). t(28)
(iii). t(-10)
(iv). The value of C, when t(C) = 212

Relation and Functions Lecture 3
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Part - 2

MISCELLANEOUS EXERCISE

Question 2. If f(x)=x^2, find \frac{f(1.1)-f(1)}{(1.1-1)}.

Question 7. Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f+g, f-g and \frac{f}{g}.

Question 8. Let f={(1,1), (2,3), (0,–1), (–1,–3)} be a function from Z to Z defined by f(x)=ax+b, for some integers a, b. Determine a, b.

Question 9. Let R be a relation from N to N defined by R = {(a, b) : a, b N and a = b2}. Are the following true?
(i). (a, a) ∈ R, for all a ∈ N
(ii). (a, b) ∈ R, implies (b, a) ∈ R
(iii). (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.

Question 10. Let A={1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)} Are the following true?
a. f is a relation from A to B
b. f is a function from A to B.
Justify your answer in each case.

Question 11. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify your answer.

Question 12. Let A = {9, 10, 11, 12, 13} and let f : A→N be defined by f (n) = the highest prime factor of n. Find the range of f.