# Relations and functions Worksheets with solutions

## Fill in the blank

(a) The Cartesian product $P \times P$ 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 g(x)=6x2+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=x2} is a relation but not function
(12) The ordered pair {(x,y)| x=3 and y is real number} is a relation and function

## 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 $A \times B$
(ii) How many number of relations can be found from $A \times C$
(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

2. Let n (A) = m, and n (B) = n. Then the total number of non-empty relations that can be defined from A to B is
(a) $m^n$
(b) mn- 1
(c) $2^{mn} -1$
(d) $n^m -1$

3. The domain and range of real function f defined by f (x) = $\sqrt {x −1}$ is given by
(A) Domain = (1, ∞), Range = (0, ∞)
(B) Domain = [1, ∞), Range = (0, ∞)
(C) Domain = [1, ∞), Range = [0, ∞)
(D) Domain = [1, ∞), Range = [0, ∞)

4. If $f (x) = x^3 - \frac {1}{x^3}$ then $f (x) + f(\frac {1}{x})$
(a) 0

(b) $2x^3$
(c) 1
(d) $\frac {2}{x^3}$

## Subjective question

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

## Link type comprehension

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

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