Page 22 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
12. Given g(x) = x + 2 and fg(x) = x + 4x + 5. Find the 2. Conversely, if Mimi wants to know how long
2
function f. she can talk for a specific total charge, she can
13. A function f is defined as f : x → 3x + 5. Find the find the inverse of the function by making T the
function g, such that the composite function gf is subject of the formula, such as
defined by gf : x → 9x + 33x + 31. C – 40
2
1 T(C) = 8
14. A function f is defined by f : x → – , x ≠ 0.
x
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(a) Express f (x), f (x) and f (x) in the simplest For example, for a total charge of 80 cent,
2
3
4
form. 80 – 40
(b) Hence, deduce the outcomes of f (x) and f (x). T(80) = 8
25
8
1 + x = 5 minutes
15. A function f is defined by f : x → , x ≠ 1.
1 – x
Generate an expression in a similar form for 3. The above example is the idea of the application Form 4
(a) f (b) f (c) f 37 of inverse functions in daily life.
2
4
1
16. A function f is defined by f : x → , x ≠ 0. 4. In function notation, an inverse function of f(x)
x 2
–1
(a) Express f (x), f (x) and f (x) in the simplest can be written as f (x).
4
3
2
form. 5. If f : x → y, then f : y → x
–1
(b) Hence, deduce the outcomes of f (x) and –1
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f (x). or if f(x) = y, then f (y) = x
31
17. Encik Karim is a sales representative of a f
chemical company. He is paid a monthly salary of
RM4 500 and extra bonus of 6% on the total sales
that exceeds RM15 000. x y
f(x) = x – 15 000 f –1
g(x) = 0.06x
h(x) = 4 500 + x
SPM Tips
Based on the information above, and given that x
exceeded RM15 000 in a specific month, Note that the −1 in an inverse function f does not
–1
(a) which function represents Encik Karim’s bonus? mean the reciprocal of f, which is f ≠ 1 .
–1
fg(x) or gf(x)? f
(b) write a composite function which represents the
total income received by Encik Karim in that
month.
(c) determine Encik Karim’s total income for that 22
month if his total sales was RM28 000.
In the following arrow diagram, x h y
the function h maps x to y. 7
1.3 Inverse Functions Determine 6 a
(a) h (6)
–1
(b) the value of a if h (4) = 7. 2
–1
A Describing the inverse of a function
Solution
1. For Mimi’s overseas phone call to Malaysia, –1
the charge is 8 cent per minute and a service (a) h (6) = 2 If f(x) = y, then
–1
charge of 40 cent. The relationship between the (b) If h (4) = 7 f (y) = x
–1
total charge and talk time is given by a function then, h(7) = 4
C(T) = 8T + 40, where C(T) is the total charge,
in cent, for a phone call lasting T minutes. Based on the arrow diagram, h(7) = a.
Therefore, a = 4.
For example, if Mimi talks for 5 minutes,
C(T) = 8(5) + 40 Try Question 1 in ‘Try This! 1.3’
= 80 cent
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