Answers290P1^
2 (i) 6
(ii) 15
(iii) 20
(iv) 15
(v) 1
(vi) 220
3 (i) 56
(ii) 210
(iii) 673 596
(iv) − 823 680
(v) 13 440
4 (i) 6 x + 2 x^3
5 16 x^4 − 64 x^2 + 96
6 64 + 192 kx + 240 k^2 x^2
7 (i) 1 − 12 x + 60 x^2
(ii) −3136 and 16 128
8 (i) 4096 x^6 − 6144 kx^3 + 3840 k^2
(ii) ±^14
9 (i) x^12 − 6 x^9 + 15 x^6
(ii) − 20
10 (i) x^5 − 10 x^3 + 40 x
(ii) 150
11 (ii) x = 0, −1 and − 2
12 n = 5, a = − 21 , b = 20
13 (i) 64 − 192 x + 240 x^2
(ii) 1.25
14 (i) 1 + 5 ax + 10 a^2 x^2(ii) a = (^25)
(iii) −2.4
Chapter 4
●?^ (Page^ 108)
(i) (a) One-to-one
(b) One-to-many
(c) Many-to-one
(d) Many-to-many
Exercise 4A (Page 110)
1 (i) One-to-one, yes
(ii) Many-to-one, yes
(iii) Many-to-many, no
(iv) One-to-many, no
(v) Many-to-many, no
(vi) One-to-one, yes
(vii) Many-to-many, no
(viii) Many-to-one, yes
2 (i) (a) Examples: one 3,
word 4
(b) Many-to-one
(c) Words
(ii) (a) Examples: 1 4,
2.1 8.4
(b) One-to-one
(c) +
(iii) (a) Examples: 1 1,
6 4
(b) Many-to-one
(c) +
(iv) (a) Examples: 1 −3,
− 4 − 13
(b) One-to-one
(c)
(v) (a) Examples: 4 2,
9 3
(b) One-to-one
(c) x 0
(vi) (a) Examples: 36π 3,
92 π 1.5
(b) One-to-one
(c) +
(vii) (a) Examples: 12π 3,
12 π 12
(b) Many-to-many
(c) +
(viii) (a) Examples:
1 32 34 , 24 3
(^)
(b) One-to-one
(c) +
(ix) (a) Examples: 4 16,
−0.7 0.49
(b) Many-to-one
(c)
3 (i) (a) − 5
(b) 9
(c) − 11
(ii) (a) 3
(b) 5
(c) 10
(iii) (a) 32
(b) 82.4
(c) 14
(d) − 40
4 (i) f(x) 2
(ii) 0 f(θ) 1
(iii) y ∈ {2, 3, 6, 11, 18}
(iv) y ∈ +
(v)
(vi) (^) {^12 , 1, 2, 4}
(vii) 0 y 1
(viii)
(ix) 0 f(x) 1
(x) f(x) 3
5 For f, every value of x
(including x = 3) gives a unique
output, whereas g(2) can equal
either 4 or 6.
●?^ (Page^ 115)
(i) (a) Function with an inverse
function.
(b) f: C 95 C + 32
f−^1 : F 59 (F − 32)
(ii) (a) Function but no inverse
function since one
grade corresponds to several
marks.
(iii) (a) Function with an inverse
function.
(b) 1 light year ≈ 6 × 1012 miles or
almost 10^16 metres.