Page 21 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions

10% RM5 000 2. In the arrow diagrams below, the function f maps set
discount rebate A to set B, and the function g maps set B to set C.
RM86 000 RM77 400 RM72 400 f g
A B C
RM5 000 10%
rebate discount
RM86 000 RM81 000 RM72 900 x 3x + 2 12x + 5
(a) Using function notation, write down
(i) a function R, in terms of p, for the price of Determine, in terms of x,
the hybrid car after applying the rebate from (a) the function f,
the manufacturer. (b) the composite function gf.
(ii) a function S, in terms of p, for the price of 3. For each of the following pairs of functions,
the hybrid car after applying the discount determine the composite functions below.
from the car company. 2
(b) Interpret the composite functions RS(p) and (a) f : x → 3x – 1, g : x → 2x ,
Form 4
1
SR(p). (b) f : x → x , x ≠ 0, g : x → x + 5
(c) Find RS(86 000) and SR(86 000). Determine (i) fg, (ii) gf,
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which function gives a lower retail price for the (iii) f , (iv) g .
hybrid car. Explain your answer. 4. For each of the following pairs of functions,
Solution determine the composite functions below.
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(a) (i) R(p) = p – 5 000 (a) h : x → x + 1, g : x → AB x , x . 0
(ii) S(p) = 0.9p (b) h : x → |x|, g : x → x – 6
(i) hg, (ii) gh.
(b) RS(p) is the price of the hybrid car after a
10% discount is given, followed by a rebate of 5. In the diagram on the
RM5 000. right, the function f x f y g z
SR(p) is the price of the hybrid car after a rebate
Penerbitan Pelangi Sdn Bhd. All Rights Reserved. k
maps x to y such that
of RM5 000 is given, followed by a discount of y = x – 4, while the
10%. function g maps y to 6
z such that z = y – 1.
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(c) RS(86 000) = R[0.9(86 000)] Find p
= R(77 400) (a) the values of p
and k,
= 77 400 – 5 000 (b) an expression for gf(x).
= RM72 400
SR(86 000) = S[R(86 000)] 6. In the diagram on the x h y g z 12
= S(86 000 − 5 000) right, the function h maps
x to y, while the function
= S(81 000) g maps y to z. Determine
= 0.9(81 000) (a) h(3), 8
= RM72 900 (b) gh(3). 3
Hence, RS(86 000) gives a lower price for the 2
hybrid car. This is because an initial discount of 7. Given the functions f : x → (x – 2) – 3, x . –2 and
3x + 5
10% will give rise to a smaller value compared g : x → x – 3 , x . 3. Determine the composite
to an initial rebate of RM5 000. function fg(5).
Try Question 17 in ‘Try This! 1.2’ 8. Given f(x) = x + 3 and fg(x) = 2x + 6, find the function g.
9. If f(x) = x + 1, find the function g such that
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Try This! 1.2 fg(x) = 2x + 3x + 5.
10. Given a function f : x → 2x – 3. Another function, h,
1. Use arrow diagrams to represent the following such that fh : x → 4x – 9. Find the function h.
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composite functions.
(a) gh(x) (b) hg(x) 11. Given g(x) = x + 2 and fg(x) = x + 9. Find the
(c) gg(x) (d) h (x) function f.
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