Page 298 - Matematik Tambahan Tingkatan 4 KSSM

4
6. (a) y (b) a = 1, b = 4 8. (a) V = –πr 3 (b) 0.49 cm
r 3
f
y = f ( x ) Bʹ(10, 3)
−1
x
0
Aʹ(2, − 1)
f –1
Latih Diri 1.10
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x + 5 3 L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
–1
–1
1. (a) f : x → (b) f : x → , x ≠ 0
2 x 1. (a) (i) 1 (ii) 6, 8, 9
4 + x 6x
–1
–1
(c) f : x → , x ≠ 0 (d) f : x → , x ≠ 5 (b) Ya kerana setiap objek hanya mempunyai satu
x x – 5 imej.
8x + 9 x – 3
–1
–1
(e) f : x → , x ≠ 1 (f) f : x → , x ≠ 1 (c) Domain = {2, 6, 7, 8, 9}
x – 1 2x – 2 Kodomain = {1, 4, 5}
1 3
–1
2. (a) f (4) = (b) x = – , x = 1 Julat = {1, 4}
3 2 2. (a) m = 35 (b) h : x → x − 1
2
5 1
3. a = – , b = 3. Fungsi tetapi bukan fungsi satu dengan satu.
2 8 4. (a) y
x – 7
4. (a) f : x → (b) f : x → 2 – 5x 4 f ( x ) = x − 3
6
3x
(c) f : x → , x ≠ 3
x – 3 x
( ) − 1 0 3 7
1
5. (a) k = 2 (b) g 2 = –6 Julat fungsi f ialah 0 f (x) 4.
Latihan Intensif 1.3 (b) 1 x 5
(c) y y = 2 x − 3

1. (a) f(2) = 5 (b) g(5) = 8 4 f ( x ) = x − 3
–1

(c) gf(2) = 8 (d) f (5) = 2
–1
–1 –1
(e) g (8) = 5 (f) f g (8) = 2
x
2. (a) Ya (b) Ya − 1 0 3 7
(c) Tidak − 3
3. (a) y x = 2
(2, 4)
5. (a) h = 7, k = 6 (b) 43
6. m = 3, c = –13
–1
f −1 Domain bagi fungsi f x + 2
–1
(4, 2) ialah 0 x 2. 7. (a) (i) f (x) = (ii) g(x) = 2x + 5
f 3
(b) x = –8
x 8. (a) k = 1 (b) m = 2, n = 1
0 (c) f (x) = x (d) f (2) = 3
2
–1
(b) y 9. (a) (i) Fungsi selanjar (ii) – 4 f (x) 4
4 (b) Tiada fungsi songsang
1
–1
f –1 10. (a) Syarat x 0. (b) f (x) = x, f (x) = x
–1
4
Domain bagi fungsi f
2 ialah 0 x 4. 11. Graf tidak semestinya bersilang pada garis y = x jika
f −1 graf bagi suatu fungsi dan songsangannya bersilang.
Kedua-dua graf ini mungkin bersilang pada garis
x
0 2 4
yang lain.
(c) y 12. (a) (i) f (x) = 8 + 5x , x ≠ 1
–1
(4, 8) x – 1
–3 – 4x
–1
(ii) f (x) = , x ≠ 2
–1
f (8, 4) Domain bagi fungsi f −1 x – 2
ialah 0 x 8. (b) f = f jika a = −d
f −1 13. (a) (i) (ii)
Julat f ialah
x y = x
0 3 –1 f (x) 3 dan
–1
–1
4. (a) h = 5 (b) f (3) = 14 f –1 domain f ialah
(c) m = –9 2 ( 0, 2 ) –1 x 3.
3x – 2 f
5. (a) h(x) = , x ≠ 0 (b) x = 2 1
x ( 2, 0 )
6. x = –5, x = 2 –1 0 1 3
20
–1
7. (a) f (x) = 220 – x (b) 173.4 –1
17
290