Page 53 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Answer Additional Mathematics

7. (a) y 2. (a) –2  f(x)  6 19. g(x) = 9x + 38
(b) Horizontal line test cut the
Q(5, 9) 5
graph only at one point.
y = x 5 – 3x
Thus, the functon f(x) has 20. (a) g(x) =
an inverse function. 2
M(a, b) Q ′(9, 5) (b) –14
f(x) 3. (a) Yes because each object in –x – 1
–1
f (x) 21. (a) f(x) =
x set K has one image in set L. 6
P(0, –5) 0 (b) (i) 12 (ii) 2 43
(c) Domain = {–3, 2, 3, 5} (b) –
P ′(–5, 0) 13
(b) a = 4, b = 1 Codomain = {5, 10, 12, 15} 22. Has an inverse function
x 1 Range = {5, 10, 12, 15}
–1
8. (a) f (x) = (b) – 5 23.
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10 10 4. (a) –29 (b) y
x + 9 12
–1
9. (a) f (x) = 13 9
2 5. (a) m = , n = 19
(b) 8 9 4 2 y = x
–1
10. (a) f (x) = x + 7 (b) x = 9
3 2
(b) 4 1 2
–1
11. (a) g (x) = 5 , x ≠ 2 6. (a) 6 (b) 12 0 x
x – 2 –3 2 9 19
20 7. (a) –2 –3
(b) – (b) 1
7 (c) –1  x  5 Domain of f : 1  x  19
–1
3x Range of f : –3  f(x)  2
–1
–1
12. (a) h (x) = , x ≠ 4 8. 13
x – 4 2 24. (a)
3x 9. –6 and f
(b) , x ≠ 2 3
x – 2 14
x + 8 1 10. y y = x
–1
13. (a) h (x) = , x ≠
2x– 1 2 f(x)
19 6
(b) –1
21 5 2 f (x) FORM 4 ANSWER
–1
14. (a) g (x) = x , x ≠ 1 0 x
x – 1 2 2 14
3
(b) (b) a = 2, b = 14
2 0 1 x x + 1
3 –7 –5 25. (a) (i)
–1
15. (a) g (x) = , x ≠ 5 Range: 0  f(x)  6 4
5 – x 7x – 5
1 11. (ii) g(x) =
(b) y 4
3 (b) 6
14 16 x – 1
16. (a) 26. (a) g (x) =
–1
5 4
9 10
(b) f(x) = , x ≠ 1 (b) fg(x) = 4x – 1
x – 1 27. (a) 6
24 5 2x – 9 11
17. (a) – (b) gf(x) = , x ≠
13 0 x 11 – 2x 2
(b) f(x) = 5x , x ≠ –3 –5 – 10 2 28. 3
3
3 + x Range: 0  g(x)  16 4
7
18. (a) 12. (a) –9 29. (a) Wrong because a = 21.
6 4 –1 x – 41
(b) g(x) = 4 – 3x (b) – 3 (b) g (x) = 24
1 11
19. (a) (c) gf(x) = 23 – 12x 30.
6 5
2 – 2x 13. h = 32k – 6
(b) g(x) = , x ≠ 0 5x
x 14. n = 5p – 2 31. (a) P(x) = , x ≠ –1
15. p = 6 – 5pq 1 1 + x
16. g(x) = 1 – 2x (b) 9
Paper 1 17. g(x) = 6x – 11 32. (a) g (x) = x + 9
–1
8x – 35
4
1. (a) –3 (b) – 1 18. g(x) = 3 35
5 (b)
6
435