**Fill in the blank**

(a) The Cartesian product P × P has 9 elements among which are found (–2, 0) and (0, 2). the set P is ……… and the remaining elements of P × P.……….

(b) The function f(x) is defined as x

^{2} . The value of $ \frac {f(2) -f(1)}{2-1}$ …..

(c) The function p(x)=x+1 and q(x)=2x-1.The value (f/g)x is ……

(d) The Function q(x)=6x

^{2}+3x-2 The value of g(-1) is ………….

**True or False statement**

(1) The relation defined as {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} is a function

(2) The relation defined as {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} is not a function

(3) The relation defined as {(1, 3), (1, 5), (2, 5)} is a function

(4) The below graph is not a function

(5) A function are relations but all relations are not functions

(6) A function is defined as

$f(x) =- \sqrt {-2x+5)}$

The domain is x≤ 5/2 and Range is f(x) ≤ 0

(7) P= {1,2,3} Q={e,f}. The total number of relation from P × Q is 64

(8) The below graph is a function

(9) The below graph is not a function

(10) The ordered pair {(x,y)|y < 3x+1} is a function

(11) The ordered pair {(x,y)|y=x

^{2}} is a relation but not function

(12) The ordered pair {(x,y)| x=3 and y is real number} is a relation and function

Solution
**Subjective Questions**
Find the domain and range of the following real function:

**(1) **y=x

^{2}
**(2) **y=-|x|

**(3) **y=3x-7

**(4) **y=-x

^{4}+3

**(5) **$y= \sqrt {2-x)$

**(6) **$y =\frac {1}{ \sqrt {11-x}}$

**Linked Type comprehension**
If A= {1,2,3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} D = { 17,19,21,23} and E={1,-1} find

**(i) **What is the number of element in A × B

**(ii) **How many number of relations can be found from A × C

**(iii) ** The mapping defined as {(1,11),{1,13},{2,7},{5,11} is a function from A × B,State True or False

**(iv) **The mapping defined as {(11,17),{13,19},{15,21},{15,23} is a Relation from C × D, State True or False

** (v) **Find the value of B × C and C × B

**(vi) **Find the value of E × E × E

**(vii) **Verify that A × (B ∩ C) = (A × B) ∩ (A × C)

**(viii) **A X B is a subset of A X C. State True or false

**(ix) **(A X B) ∩ (B ∪ D)

**Mulitiple Choice questions**
1) Given the relation R = {(6,4), (8,-1), (x,7), (-3,-6)}. Which of the following values for x will make relation R a function?

a)8

b)6

c) -3

d) 1

Solution
Solution (d)

**Subjective question on number of elements**
1) What is the domain and range in the relation shown in below mapping

2) Please tell if the below mapping is function or not

__Subjective Questions__
There are two functions defined as below

Let P={(0,5),(1,4),(2,3),(3,2),(4,1),(5,0)}

Q={(1,1),(2,4),(3,9),(4,16),(5,25),(6,36)}

1)What is the domain and range of P

2)What is the domain and range of Q

3) What is the domain of function (Q-P)

4) List the ordered pair of (Q-P) in set notation

5) What is the domain of Q/P

6) List the ordered pair of (Q/P) in set notation

Solution
- Domain of P ={0,1,2,3,4,5)
Range of P ={5,4,3,2,1,0}

- Domain of Q ={1,2,3,4,5,6)
Range of P ={1,4,9,16,25,36}

3. The domain of function (Q-P) is the intersection of domain of P and Q

So Domain of (Q-P)={1,2,3,4,5}

4.(1,-3),( 2,1),(3,7),(4,15),(25)

5) The domain for Q/P is {1,2,3,4} as on 5 function p is zero

6) The ordered pair of Q/P

(1,1/4),(2,4/3),(3,

9/2),(4,16)
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