Page 49 - PRE-U STPM MATHEMATICS (T) TERM 1

ANSWERS

Chapter 1 Functions Exercise 1.2
1. (b) c, d (c) {1, 2, 3, 4, 5}
Exercise 1.1 (d) {a, b, c, d} (e) No
1. (a) –9 (b) 7 (c) 0 (d) 0 2. (a) X Y
2. (a) (i) 3 (ii) 1 (iii) 0 –2 3
(b) (i) 24 (ii) 99 –1
3. (a) [–2, 6] or –2 < f(x) < 6 0 1
1
f(x ) 2 7
6 (b) {–2, –1, 0, 1, 2}
(c) {1, 3, 7}
(d) No
3. (a)
Y
x
–1 0 3
X –5
–3
–2
1 –1
(b) [–1, 3] or –1 < f(x) < 3 3 3
5 5
f(x )
7 7
3 9 11
15
(b) –1, 15
(c) Yes
x
–1 0 3 1
4. No. f(0) = f(1) = 0,
–1 2
a
1
9
9
(c) 3 – , 44 or – < f(x) < 4 5. 1 + a 2 ; {g : 0 , y < }
4 4 2
–1
f(x ) 6. (a) f : x ⟼ x + 2, x ∈ R
–1
(b) f : x ⟼ x – 1 , x ∈ R, x > 1
4
–1
(c) f : x ⟼ x + 1, x > 0
–1
(d) g : x ⟼ 3 + x + 1 , x > –1
(e) g : x ⟼ x + 9 , x . –9
–1
x
–2 0 3 2 + 3x
(f) h : x ⟼ x , x ≠ 0
–1
–1
– 9 _ (g) h : x ⟼ 2(x + 1) , x ≠ 1
4 x – 1
1 – x 1
–1
4. (a) No (b) Yes (c) No 7. f (x) = 2x – 1 , , x < 1
2
1
5. (a) 1, 4, , 64 (b) 4 (c) R +
2 9. (a) f(x ) (b) f(x )
6. x + 2 f f –1
7. 4 – x 2 f –1 f
8. (a) cos (1 + x) (b) cos (cos x) x 0 x
(c) 1 + cos x 0
9. (a) 1 – x , –1 , x , 1 (b) 1 – x
2
2
(c) 2x – x 4
2
10. (a) 4x – 6x + 1 (c) f(x ) f (d) f(x ) f
(b) 2x + 6x – 1 f –1 f –1
2
(c) 4x – 9
(d) x + 6x + 14x + 15x + 5 x x
4
2
3
0 0
11. (a) 6 (b) 25
(c) 2a – 4a + 9 (d) 4x – 12x + 14
2
2
2
(e) 2x + 4x + 9 (f) x + 10x + 30
4
2
268
Answers STPM Math T S1.indd 268 3/28/18 4:25 PM