Free Printable Relation and Function

1.

Let R be a relation on N given by R={(x,y):x=y-2, y>6}, then

a)

(2,4)∈R

b)

(3,8)∈R

c)

(8,7)∈R

d)

(6,8)∈R

2.

If A={a,b,c} theen R={(b,c)}, then R is

a)

Reflexive only

b)

Symmetric only

c)

Transitive only

d)

equivalence relation

3.

Let A={1,2,3}, and R is {(1,1),(1,2),(1,3), (2,2), (2,3), (3,3)}, then R is

a)

reflexive but not symmetric

b)

reflexive but not transitive

c)

symmetric and transitive

d)

neither symmetric nor transitive

4.

For real numbers x and y define xRy iff x-y+√2 is an irrational number. then R is

a)

reflexive

b)

symmetric

c)

transitive

d)

none of these

5.

The domain of R={(x,y): x²+y²≤4, x,y∈ Z}

a)

{0,1.2}

b)

{0,-1,-2}

c)

{1,2}

d)

none of these

6.

the maximum number of equivalence relation in set A={1,2,3} is

a)

1

b)

2

c)

4

d)

5

7.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

8.

Find the inverse of f(x) = 3x +8

a)

$f^{-1}\left(x\right)=3x-\frac{8}{3}$

b)

$f^{-1}\left(x\right)=\frac{8}{3}x-\frac{1}{3}$

c)

$f^{-1}\left(x\right)=\frac{1}{3}x-\frac{8}{3}$

d)

$f^{-1}\left(x\right)=\frac{1}{3}x+\frac{8}{3}$

9.

If f(x)=2x-1 and g(x)=x²-2x+1, what is f(g(x))?

a)

2x²+4x+1

b)

2x²-4x-1

c)

2x²-4x+1

d)

2x²+4x-1

10.

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

a)

Reflexive and Symmetric

b)

Transitive and symmetric

c)

Equivalence

d)

Reflexive, transitive but not symmetric

11.

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is

a)

144

b)

12

c)

24

d)

64

12.

Let A=[-1,1], then the mapping given by $f:A\rightarrow A$

f(x) = x|x| is

a)

one one but not onto

b)

onto but not one one

c)

bijective

d)

none of these

13.

$Let\ f\left(x\right)=\frac{1}{1-x},\left(x\ne1\right)\ then\ fofof\left(x\right)\ =$

a)

$\frac{1}{\left(1-x\right)^2}$

b)

$\frac{1}{\left(1-x\right)^3}$

c)

$\frac{1}{1-x}\forall x\ne1$

d)

$x\ \ \forall x\in R-\left\{0,1\right\}$

14.

Let $f:R\rightarrow A\ s.t\ f\left(x\right)=\frac{x^2}{1+x^2}\ be\ a\ surjection,\ then\ A=$

a)

R

b)

[-1,1]

c)

[0,1)

d)

[0,1]

15.

Which graph is NOT representing a function?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

16.

f(x) = (x-1)²

g(x) = 3x+4

h(x) = 3x-1

f(g(h(3))) =

a)

8

b)

28

c)

729

d)

54

17.

Are the following inverses of each other?
$f\left(x\right)=\frac{1}{3}x+3\ \ and\ \ f\left(x\right)=-3x-3$

a)

True

b)

False

18.

Find the inverse of $f\left(x\right)=-3x^2+5$

a)

b)

c)

d)

19.

let $f\left(x\right)=\left[x\right]\ and\ g\left(x\right)=\left|x\right|\ ,then\ \left(gof\left(\frac{-5}{3}\right)-fog\left(\frac{-5}{3}\right)\right)$

a)

-1

b)

0

c)

1

d)

-2

20.

$If\ f\left(x\right)=\left(x-2\right)^5+3\ then\ f^{-1}\ will\ be$

a)

$\left(x-3\right)^{\frac{1}{5}}+2$

b)

$-2+x^{\frac{1}{5}}$

c)

$\left(x+1\right)^5+3$

d)

$\left(x+2\right)^{\frac{1}{5}}-3$

21.

Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = (a)

22.

Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 4. Then R partitions the set Z into (a) pairwise disjoint subsets.

23.

$\left[\frac{1}{5}+\frac{1}{1000}\right]+\left[\frac{1}{5}+\frac{2}{1000}\right]+\left[\frac{1}{5}+\frac{3}{1000}\right]+...+\left[\frac{1}{5}+\frac{999}{1000}\right]=$ where [x] represents integral part of x

a)

199

b)

200

c)

201

d)

200.5

Relation and Function

Total questions: 23

Worksheet time: 29mins

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