Unit 9
Relation and Function
PRACTICE QUESTIONS: UNIT 9 (Relation and Function)
1. Draw the mapping diagram of
for the domain -3 to 2. State the type of
mapping. Not in mind how to do this
Ans:
f(x)=3x²+4
For x = -3, f(x)=31
For x = -2, f(x)=16
For x = -1, f(x)=7
For x = 0, f(x)=4
For x = 1, f(x)=7
For x = 2, f(x)=16
It is onto mapping
2. Given the relation set {(0, 4), (3, 5), (6, 6), (9, 7), draw the mapping diagram and
determine the rule of the relation.
Solution:
Let:
X
Y
0
3
4
5
6
6
9
7
1
Unit 9
Relation and Function
As, every element of set X is corresponds with one element of the set Y so this is ‘1 1’Correspondence
3. Given
i.
Determine
Solution:Let y = 3x – 2
y + 2 = 3x
x=
So,
=
ii.
Hence, solve the equation
3x 2 = 4
3x = 4 + 2
3x = 6
x=2
4. The function
I.
1
Find the value of
Solution:1
Put x = 0, then
1
1
1
2
Unit 9
Relation and Function
ii.
Find the value of
for which
1
Put x =- , then
1
1) Given that
and
i.
g(-5)
Solution:


ii.

Let y = x + 3
y 3 =x
So,
=x 3
Now put x = 7
=7– 3= 4
iii.

Put x =0;
Calculate:


Now put the value of ‘g’ in h(x):= x2
= (3)2
=9
3
Unit 9
Relation and Function
2) The functions
and , are defined by
1 and
1.
a) Calculate g(-3)
Solution:
1
Put x = 3

1

–1

b) Find, in its simplest form
i.
Solution:-
1
Let y =
1
y=
3y = x +3
x = 3y 3
So,
= 3x -3
iii.
Solution:1
Let y = 2x – 1
y + 1 = 2x
x=
So,
=
iv.
Solution:1
And
1
Now put the value of g(x) in f(x):
=
1
=
=
4
Unit 9
Relation and Function
7. Given that
i.
and
Evaluate
Solution:
Put x =
:
and
2





Now put the value of f(-2) in g(x)
So,


ii.
Determine
Solution:
Let
y(x + 1) = 2x 3
yx + y = 2x
yx
3
2x = y – 3
x(y 2) =
x=
So,
=
5
Unit 9
iii.
Relation and Function
Calculate the value of , if
Solution:
1 .
1
So,
1

 2x 3 = 12(x + 1)
 2x 3 = 12x + 12
 12x+2x = 3+12
 10x = 15
 x=
iv.
Calculate the values of x, for which:
a. f (x) = 0
Solution:So,
=0





b.
2x 3 = 0(x+1)
2x 3 = 0
2x = 3
x=
is undefined.
Solution:

Put x =
1
1
So,
1 = undefined
6
Unit 9
Relation and Function
8. Given that
i.
Calculate the value of
Solution:Put x =
ii.
and
1:
.
2 then,
Write an expression for
Solution:
in its simplest form.
1
and
then put the value of f(x) in g(x):



iii.
Find the inverse function
Solution:
.
Let y =
5y = 2x +1
5y – 1 = 2x
x=
So,
=
7
Unit 9
Relation and Function
9. Given
,
i.
,
The value of
Solution:
, find
,
Put x = 3 then,



1
Now,
Put x = 2

1
:-

Now for
1
ii. An expression for
Solution:
.
and
Now put the value of g(x) in f(x)
Now for g f (x):
8
Unit 9
Relation and Function
10. Given that
i.
,
Evaluate
Solution:
Put x =
and
:
and
6 then:
1
Now for f g (3):
11
Put the value of g (3) in f(x):
So,
11
ii.
If
, calculate the value of .
Solution:
1

9
Unit 9
iii.
Relation and Function
Obtain an expression, in terms of , for
Solution:
.
1
1
y(2x 1) = 5x+1
2xy y = 5x+1
2xy 5x = y+1
(2y 5)x = y+1

10