Lecture 3 Class 11 Relations and Functions

Lecture - 3 Chapter 2 Relations and Functions

“Don’t be afraid to give up the good to go for the great.” – John D. Rockefeller

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

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

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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.

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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.

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