Page 63 - Mathematics_Form_3

Functions
y = x 2

x
2
y =
Example 2.29 Making y the subject gives,
Find the inverse of the function y = ± x .
f (x) = 3x + 7 and draw the graphs of Thus, f − 1 ( )x = ± . x
both functions on the same xy- plane. The graphs of both functions are
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Solution shown in the following figure.
Let y = f (x) , that is
y
y = 3x + 7. 4
Interchange x and y to obtain,
3
x = 3y + 7.
Making y the subject gives, 2

y = − . 1
x _
7 _
3 3
Thus, f (x ) = − . -3 -2 -1 0 1 2 3 4 x
x _
7 _
−1
3 3
The graphs of both functions are shown -1
in the following figure. -2
y
8 f(x)= 3x+7 The inverse of ()fx = x is not a function
2
7
6 because each value of , has two values
5 of y.
4
3
2 Remark: Inverses of some functions
1 are not functions unless the
x
-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 domains are restricted. For instance,
-1
2
, x ≥
0 . However, the
fx
() =
x
-2 inverses of all one-to-one functions
Mathematics for Secondary Schools Example 2.30 Example 2.31
-3
-4
are functions.
Find the inverse of the function
Find the inverse of the function
2
4x −
() =
fx
x , then draw its graph and its
2
fx
() =
3
inverse on the same xy- plane. State
whether the inverse is a function.
Let y =
() . It implies,
Solution
4x − 2
Let y = x , then Solution fx
, interchange and to get
2
_
y =
3
2
x
y =
interchange x and y to obtain, 4y − 2
2
y =
x
_
2
y = y = ± x x = 3 .
x.
y = ± x
56 Student\s Book Form Three
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MATHEMATIC F3 SB.indd 56 18/09/2025 09:59:03
MATHEMATIC F3 SB.indd 56