Page 29 - Mathematics_Form_3

Relations

Exercise 1.7 5. R = {(x, y ): y = 2x + 1} .

In questions 1 to 3, find the inverse of 6. R = {(x, y ): 2y − 1 = 4x} .
each of the given relations. 7. R = {(x, y ): y = x } .
2
1. R is the set of all pairs of coordinate
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8. R = {(x, y ): y < 0} .
points in the xy - plane.
9. R = {(x, y ): 3x > y} .
2. R is the set of all ordered pairs (x, y)
of real numbers where y is the cube 10. R = {(x, y ): 2x + 5 < y} .
root of x . 11. R = (x, y ): y = _ }
2
.
{
x + 5
3. R is the set of all pairs of coordinate 12. R = {(x, y ): y = 3 x − 1} .
2
points in the xy-plane which lie
below the line y = 4 .
4. Study the relation R shown in the Graphs of inverse relations
following figure and answer the Consider the relation

subsequent questions. R = {(x, y ) : y > x} . Its inverse is given
R by R = {(x, y ) : y < x} . In this case, R
−1
is the relation “greater than” for all real
a p numbers, while R is the relation “less
−1
b q than” for all real numbers.
c r The graphs of R = {(x, y ) : y > x} and
−1
d s R = {(x, y ) : y < x} are shown in the
e shaded regions in Figure 1.9 and Figure
1.10, respectively. y 4

Mathematics for Secondary Schools (b) Make a list of all ordered pairs -5-4 -3 -2 -1 0 3 2 1 1 2 y = x 4 x
(a) Make a drawing to show the
−1
inverse relation R .

−1
belonging to R .
(c) Which set is the domain of R ?
−1
3
-1
(d) Which set is the range of R ?
−1
-2
In questions 5 to 12, find:
-3
-4
(a) The inverse of a relation.
-5
(b) The domain and range of the
inverse of a relation. Figure 1.9: Graph of the relation
R = ( { x, y ) y >: x }

22 Student\s Book Form Three

18/09/2025 09:58:45
MATHEMATIC F3 SB.indd 22
MATHEMATIC F3 SB.indd 22 18/09/2025 09:58:45