Page 61 - Mathematics_Form_3

Functions

Exercise 2.7 Inverse of a function
In Chapter One, you learnt about the
In questions 1 to 8 draw the graph
of each of the functions and give its inverse of a relation. The inverse of
a function is also a function provided
domain and range: that the function is one-to-one. Study
() =
1. fx 1 x− Figure 2.7 and Figure 2.8 and learn how
() =
2. gx − 2x + 3 to differentiate a one-to-one function
from its inverse.
() =
3. gx 2 − x
() =
4. fx x − 1 a 1 1 a
() =
5. gx 1 − x − 2 b 2 2 b
() =
6. hx x + 2 + 4 1READING ONLY 3 c
c
3
2
( ) =
7. fx 3x + 2; x ≥−
3
4 Figure 2.7: Pictorial representation of a
( ) =
8. fx 3x − 4 1; x+ ≤ one-to-one function
3
9. Given ()fx = 1 2 ;x x− ∈ . 
FOR ONLINE
a 1 a
(a) Find the range of ( ).fx

b
(b) Draw the graph of ( ).fx 2 2 b
(c) From the graph, explain why 3 c
c
3
() it is not a one-to-one
fx Figure 2.8: Pictorial representation of the
Mathematics for Secondary Schools 10. Given ( )hx = 5x − 10 ; x ≥ k The inverse function reverses the
function.
(d) Find the domain for ()fx for

which it will become one-to-
inverse of a one-to-one function
one function.

direction of the arrows. Figure 2.7 shows
where k is a constant.
a one-to-one function. Figure 2.8 is the
(a) State the smallest possible
inverse of the function presented in
value of k for which ()hx to
be one-to-one.
inverse takes each domain value to only
(b) When k has the smallest Figure 2.7. It can be observed that the
one range value, hence it is a function.
possible value draw the graph Figure 2.9 represents a many-to-one
of ( ).hx function. In Figure 2.10, It can be
observed that the inverse takes one input

54 Student\s Book Form Three

18/09/2025 09:59:02
MATHEMATIC F3 SB.indd 54
MATHEMATIC F3 SB.indd 54 18/09/2025 09:59:02