Page 14 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
Step II: Reflect the negative part of the graph on the 2. Conversely, if the image is given, then the value
x-axis. of the object can be determined as well.
For example, when the value of the image is 4,
y
f(x) = 4
y = |–x – 1| 3x – 2 = 4
1
1 2 3 x = 6
x x = 2
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0 2
–1 Therefore, the object is 2.

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Step III: When x = −2, y = 2. When x = 8, y = 3. The
2
graph is a V-shaped graph with the vertex at Given the function f(x) = x + 4x. Find the image Form 4
(2, 0). when the object is
(a) −2
y (b) 3t
y = |–x – 1| (c) x + 1
1
3 2
2 Solution
Range (a) f(x) = x + 4x
2
x f(−2) = (−2) + 4(−2)
2
–2 0 2 8 = −4
Domain
(b) f(x) = x + 4x
2
The range is 0 < y < 3. f(3t) = (3t) + 4(3t)
2
= 9t + 12t
2
Try Question 10 in ‘Try This! 1.1’
(c) f(x) = x + 4x
2
f(x + 1) = (x + 1) + 4(x + 1)
2
C Determining the image of a function = x + 2x + 1 + 4x + 4
2
when the object is given, and vice = x + 6x + 5
2
versa
Try Questions 11 – 13 in ‘Try This! 1.1’
1. To determine the image of a function when the
object is given, substitute the value of the object
in that function. 11
For example, for the function f(x) = 3x – 2, Given the function g(x) = 7x – 2. Find the object
then f(4) = 3(4) – 2 which has an image
= 10 (a) 19
4 is the object and 10 is the image. (b) 3x
2
(c) which is the same as the object under the
Input x = 4
(object) mapping of the function g.
Solution
(a) Let x be the object which has an image of 19.
Multiply the
input with 3 Therefore, g(x) = 19
and then 7x – 2 = 19
minus 2.
7x = 21
x = 3
Output = f(4)
(image)

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