# Lecture - 3 Chapter 2 Relations and Functions

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

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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*)=2*x *– 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*) = 2*x* – 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 *= *b*^{2}}. 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*.