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

(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) 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

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

Solution

(1) y=x

(2) y=-|x|

(3) y=3x-7

(4) y=-x

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

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

(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)

(a) 8

(b) 6

(c) -3

(d) 1

Solution

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) $n^m -1}$

Solution

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, ∞)

Solution

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

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 Download Relations and functions class 11 Worksheets as pdf

- Cartesian Products
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- What is relations?
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- What is Function
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- Domain of Function
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- Range of Function
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- Identity Function
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- Constant Function
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- Linear Function
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- Modules Function
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- Greatest Integer Function
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- Polynomial Function
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- Algebra of Real Function

Class 11 Maths Class 11 Physics