Page 15 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
(b) Let x be the object which has an image of 3x . 13
2
Therefore, g(x) = 3x 2
7x – 2 = 3x 2 The temperature of the surface of a lake is 22°C on a
3x – 7x + 2 = 0 specific day. A diver finds that the temperature of the
2
(3x – 1)(x – 2) = 0 water reduces by 1.2°C for every 6 m he dives to the
1 bottom of the lake.
x = or 2
3 (a) Using function notation, represent the temperature
of the water with respect to the depth of water.
(c) Since the image of the object x is x, (b) Using the function notation in (a), find the
g(x) = x temperature of the water at a depth of 45 m.
7x – 2 = x (c) The temperature of water at the bottom of the
6 x = 2 lake is 5.5°C. What is the depth, in m, of the lake?
1
x =
3 Solution
(a) Let d represents the depth, in m, from the surface
Form 4
Try Questions 14 – 16 in ‘Try This! 1.1’ of the lake, while T represents the temperature,
in °C, at a specific depth.
d
12 T(d) = 22 – 1.2 1 2 The temperature reduces
6
by 1.2°C for every 6 m.
Given f : x → | 2x – 6 |. Find 45
(a) f(−1) (b) T(45) = 22 – 1.2 1 2
6
(b) the values of x if f(x) = 4. = 13
The water temperature at a depth of 45 m is
Solution 13°C.
(a) f(x) = | 2x – 6 |
(c) T(d) = 5.5
f(−1) = |2(–1) – 6 |
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d
= | –8 | 22 – 1.2 1 2 = 5.5
6
= 8 d
1.2 1 2 = 22 – 5.5
6
(b) f(x) = 4 1.2d = (6)(16.5)
| 2x – 6 | = 4 99
2x – 6 = 4 or 2x – 6 = –4 d = 1.2
2 x = 4 + 6 2x = 2 = 82.5 m
2 x = 10 x = 1
x = 5 The depth of the lake is 82.5 m.

Alternative Method Try Question 19 in ‘Try This! 1.1’
y
8 Try This! 1.1
7
6 1. The arrow diagram below represents a function
5 which relates the time (p.m.) with temperature (°C).
4 f(x) = 4
Time (p.m.) Temperature (°C)
3
x = –1 12 35
2 1 5 30 27
1 2 33 31 28
x 3 32
–2 –1 0 1 2 3 4 5 6 4
6 31 34
29
Try Questions 17 – 18 in ‘Try This! 1.1’ Set A Set B

12