Page 27 - ACE YR IGCSE A TOP APPR' TO ADD MATH

(b) −2 < f(x) < 8 (c) f(x) > 5
[1] [1]
(c) |3x – 4| – 2 = 3 (d) It has no inverse because it is not a one-to-one
|3x – 4| = 5 function.
3x – 4 = 5 or 3x – 4 = –5 x > −2
x = 3 or x = – 1 [2]
3 [2] 18. (a)

(d) x > 4 y y = f(x)
3 [1]
15. (a) y
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y = f (x)
–1

9 0.5
0.5 x

x [3]
1 9 (b) gf(x) = −(2x − 1) − 2(2x − 1)
2
[3] = –(4x – 4x + 1) – 4x + 2
2
(b) 0 < f(x) < 16 = –4x + 1
2
[1] Maximum value of gf(x) = 1
(c) k = 5 [3]
[1] (c) –x – 2x = (x + 2x + 1 – 1)
2
2
2
16. (a) f(x) > –5 = –(x + 1) + 1
[1] a = 1, b = –1 [2]
2
(b) (i) 1 1 2 , –5 (d) Let y = h (x)
–1
[1] h(y) = x 2
2
(ii) 1 1 2 , 5 –(y + 1) + 1 = x
(y + 1) = 1 – x
2
–1
[1] h (x) = –1 + √1 – x
[2]
17. (a) x + 4x + 2 – 2 + 9 19. (a) g(6) = 2 – 6
2
2
2
= (x + 2) + 5 = –4
2
a = 2, b = 5 [1]
[2] 1
(b) x = –2 (b) 3(s – 2) + 1 = (–4)
3
y 3s – 6 + 1 = – 4
14 3
3s – 5 = – 4
12 3
3s = 11
10 3
11
8 s =
9 [2]
6
(c) g(3x + 1) = 2 – (3x + 1)
4 = 2 – 3x – 1
= 1 – 3x
2 [2]
(d) fg(x) = 3(2 – x) + 1
x
–4 –2 0 2 fg(x) = –3x + 7
when x = –2, |fg(x)| = 13
[3]
when x = 4, |fg(x)| = 5

Answers 167

Answers Add Math.indd 167 14/03/2022 12:29 PM