Page 11 - Praktis Hebat 2021 - Additional Mathematics F4

Additional Mathematics Form 4 Answers
f bukan suatu fungsi satu dengan satu kerana 5. (a) gh(x) = 1
dua objek yang berlainan mempunyai satu imej 2(x + 1)
yang sama. Oleh itu, fungsi f tidak mempunyai 3x – 1
fungsi songsang. hg(x) = x – 1
x + 4
32. (a) Since fg(x) = gf(x) = x, hence g(x) = 2 is an g (x) = – x – 1
2
inverse function fg(x) = 2x – 4. x – 2
x + 4 h (x) = 4x + 9
2
Oleh sebab fg(x) = gf(x) = x, maka g(x) =
ialah fungsi songsang bagi fg(x) = 2x – 4. 2 9
(b) Since fg(x) = gf(x) = x, hence g(x) = 3x – 6 is an (b) x = 3, x = – 7
inverse function of fg(x) = x + 2. 6. (a) g(x) = 4 + 11x
3
Oleh sebab fg(x) = gf(x) = x, maka g(x) = 3x – 6 (b) (i) x = – 11
ialah fungsi songsang bagi fg(x) = x + 2. 15
3 (ii) gg (x) = x, x = – 2
–1
x + 2 x – 11 5
33. (a) f (x) = (b) f (x) =
–1
–1
7 3 7. (a) k = 5, m = 4, n = 9
4 (b) x = 2, x = –1
–1
34. (a) f (x) = 5x – 5 (b) f (x) = – 2 –1
–1
x (c) Yes/ Ya, ff (x) = x
x + 1 3 (i) True because when / Benar kerana apabila
35. (a) f (x) = (b) f (–4) = – x = –2, ff (–2) = –2
–1
–1
–1
1 – x 5 (ii) False because when / Palsu kerana apabila
3x – 5
36. (a) f(x) = 2x + 1 (b) f(x) = x = 3, ff (3) = 3
–1
2
4 8. (a) (i) f(–3) = –16
37. (a) f(x) = –5x + 2 (b) x = (ii) m = 5
5
1 (iii) gf(x) = –27x + 73
38. (a) x = 3 (b) x = –
6 (b) 73
39. (a) f(3) = 2 (b) m = 12, m = 16 x –2 0 27 4
x + 5
40. f (x) = 3 y 127 73 0 35
–1
4x – 7
g (x) =
–1
3x y
x = 4 140
120
PAPER 2 100
1. (a) x –2 0 4 3 80
3 60
f(x) 10 4 0 5 40
20
f(x) x
–2 –1 0 1 2 3 4
12
10
8 9. (a) g(x) = 2x + 3
6 –1 7x – 4
(b) g f(x) =
4 44 2
2 (c) x = – 21
x
0
–2 –1 1 2 3 10. (a) f(x)
7 35 y = f(x)
(b) 0 < f(x) < 10 (c) x = 5, x = – 30
3 25
2. (a) g(–4) = –21 (b) g(–2) = –12 20
(c) x =2, x = 2 15
5 10
3. (a) p = 2, q = 7 5 y = f –1 (x)
(b) h(5) = 3 –10 –5 0 5 10 15 20 25 30 35 x
(c) x = 7 –5
4. (a) fg(x) = 12x – 4x + 80
2
gf(x) = 48x – 4x + 20 (b) Domain: –7 < x < 29
2
–1
fg(x) ≠ gf(x) Range / Julat: 0 < f (x) < 6
5 (c) x = 4, x = –3
(b) x = 4, x =
3
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ANS HEBAT ADD MATH F4 1P.indd 2 09/04/2021 3:50 PM