Page 27 - Mathematics_Form_3

Relations

Finding the inverse of a relation by (y, x ) . This is because a coordinate
point is always written by starting
The inverse of a relation R which is in
with the x coordinate followed by the
the form of an equation or an inequality
y coordinate.
is obtained using the following steps:
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Example 1.22
Step 1: Interchange the variables x
and y. Find the inverse of the relation
R = {( , ): student is taller than
Step 2: Express y in terms of x.
student }.
Step 3: The resulting equation
represents the inverse of the Solution
−1
relation. The inverse relation R of the relation
R is obtained by interchanging the
variables x and y. Therefore,

−1
Example 1.21 R = {(x, y ) : student x is taller than
student y} .
Find the inverse of the relation

R = {(x, y ): y = 5x} . Example 1.23

Solution Given the relation
Interchange the variables x and y, and R = {(x, y ):y = 4 x } , find:
2
then write y in terms of x. The two steps (a) The inverse of R.
can be summarized as follows: (b) The domain and range of R . 2
−1
Mathematics for Secondary Schools Step 2: Write y in terms of x: 1  x 1 _ interchange the variables x and y to
Step 1: Interchange the variables. That
Solution
is, y = 5x becomes x = 5y.
(a) Given that R = {(x, y ) : y = 4 x } ,

get x = 4 y . Rewrite y in terms of
2
From x = 5y, it gives y = x .
x such that
5
x
x
y ±=
Û
y =
2

.
( ,xy
) : y =
Therefore, R =
1
−



5 
Hence, the inverse relation of R is
given by: 4 2
Note that: The ordered pairs belonging ì x ü
-
1
to R are denoted by (x, y) and not R -1 = í ( , yx ): y = ± 2 ý .

î þ
20 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 20 18/09/2025 09:58:44
MATHEMATIC F3 SB.indd 20