Page 25 - ACE YR IGCSE A TOP APPR' TO ADD MATH

Answers

5. y
1 Functions

1. (a) f(x) = 3 – √x + 8 10
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f(0) = 3 – √8
f(3) = 3 – √11 8

3 – √11 < f(x) < 3 – 2√2 6
[2]
(b) Let f (x) = y 4
−1
f(y) = x
x = 3 − √y + 8 2
√y + 8 = 3 − x 1
y + 8 = (3 − x) x
2
f (x) = (3 − x) − 8 –2 –1 0 1 2 3
−1
2
= x − 6x + 1 –1
2
Domain: 3 − √11 < x < 3 − 2√2
Range: 0 < f (x) < 3 [2]
−1
[4] (a) y = |4(−2)−1|
2. (a) f(0) = −4 y = |−9|
f(−10) = 496 y = 9
−4 < f(x) < 496 0 , y , 9
[3] [1]
(b) x > 0 [1] (b) 1 , c , 12
[2]
3. (a) y
6. y
12 y = |3x|

10
y = |x + 2|
6
8

6
x
–3
4
[2] (1, 3)
(b) 2x + 6 = 4 or 2x + 6 = −4 (–0.5, 1.5) 2
x = −1 or x = −5
[2] x
–6 –4 –2 0 2 4 6
2
4. x − 7x + 6 = 6 − x
x − 6x = 0 3x = x + 2 or 3x = –x – 2
2
x = 0 or x = 6 2x = 2 or 4x = –2
x − 7x + 6 = x − 6 x = 1 or x = –0.5
2
x − 8x + 12 = 0 y = 3 or y = 1.5
2
x = 6 or x = 2 (1, 3) or (−0.5, 1.5)
x = 0, 2 and 6 [3] [6]

Answers 165

Answers Add Math.indd 165 14/03/2022 12:29 PM