Page 64 - Mathematics_Form_3

Functions

3x + 2
2
2

Making y the subject gives, y = _ . x = 1 − y or y = 1 − x or
2
2
4 _
3x + 2 y = ± √ 1 − x for x ≤ 1.

2
Therefore, f − 1 ()x = .
4 Since the domain ()fx is restricted
1,
x
Example 2.32 to 0 ≤≤ then f − 1 ()x = 1 x− 2
READING ONLY
x
Find the inverse of the function for 0 ≤≤ 1.
_
f (x ) = √ x − 3 , for x ≥ 3. Therefore, f − 1 ()x = 1 x− 2 for

x
Solution 0 ≤≤ 1.
Let y = fx
() .
_
It implies, y = √ x − 3 , upon Exercise 2.8

interchanging the variables y and x
_
gives x = y − 3 . Making y the subject In questions 1 to 3, determine whether

√
of the equation leads to y = x + 3. each given function has an inverse.
2
If it does find the inverse(s) of the
2
Therefore, f (x ) = x + 3, for x ≥ 0.
−1
function(s).
2
1. f (x ) = x + 2x + 1
Example 2.33
2. f (x ) = x + 2
Find the inverse of the function 3. f (x ) = 3x − 2
FOR ONLINE
  1  
−−
F =  (1,2),(3,6),(5,10),( 2, 4),  ,1  4. Given a function
  2   gx x +− 2; x∈ .
2
( ) =
x
Solution (a) State the range of ( ).gx
The inverse of F is obtained by
interchanging the x and y coordinates (b) Sketch the graph of ( ).gx
in each point. (c) From the graph explain why
() has no inverse.
Therefore, gx
  1   (d) Suggest a domain for ()gx
−−
F =  (2,1),(6,3),(10,5),( 4, 2), 1,  . 

  2   for which it has an inverse.
In questions 5 to 10, find the inverse of
Example 2.34 each of the given functions: Mathematics for Secondary Schools
_
Find the inverse of the function 5. f (x ) = √ x for x ≥ 0
|
|
fx 1 x− 2 for 0 ≤≤ 1. 6. f (x ) = x − 2 , for x ≥ 2
() =
x
Solution 7. F = {(2, 3), (3, 4), (4, 5), (7, 6)}
Let y = fx _ 2 8. f (x ) = x
(). It implies, y = √ 1 − x ,
interchanging the variables x and 9. f (x ) = x − 2 , for x < 0
2
_
y gives x = 1 − y and hence 10. f (x ) = x + 1 , for x <− 1

2
|
|
√
Student\s Book Form Three 57
18/09/2025 09:59:04
MATHEMATIC F3 SB.indd 57 18/09/2025 09:59:04
MATHEMATIC F3 SB.indd 57