(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)=6x

Solution

(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) $y=x^2$

(2) $y=-|x|$

(3) $y=3x-7$

(4) $y=-x^4 + 3$

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

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

Solution

(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)

Solution

(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

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) $\frac {2}{x^3}$

Solution

Solution

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

Solution

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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