Page 27 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
13. Selesaikan setiap yang berikut. SP 1.3.2 TP3
Solve each of the following.

Rajah menunjukkan y (a) Rajah menunjukkan y
1
2 4 y = x graf bagi f(x) = x + 2 bagi
graf bagi f(x) = (x – 3) – 5 (–5, 3) 2 (4, 4)
bagi domain 0  x  3. y = f (x) domain –6  x  4.
–1
The diagram shows the graph The diagram shows the y = f(x)
1
of f(x) = (x – 3) – 5 for the x graph of f(x) = x + 2 for 0 x
2
domain 0  x  3. 0 3 4 2 (–6, –1) y = f (x)
–1
(i) Nyatakan domain y = f(x) the domain –6  x  4. y = x
dan julat bagi f . –5 (3, –5) (i) Nyatakan domain
−1
−1
State the domain and dan julat bagi f . (–1, –6)
range of f . State the domain and
−1
−1
(ii) Pada graf tersebut, range of f . −1
Penerbitan Pelangi Sdn Bhd. All Rights Reserved
−1
lakarkan graf bagi f . (ii) Pada graf tersebut, lakarkan graf bagi f .
−1
On the graph, sketch the graph of f . On the graph, sketch the graph of f .
−1
−1
(i) Domain f ialah –5  x  4 (i) Domain f ialah −1  x  4
−1
–1
Domain of f is Domain of f is
–1
−1
Julat f ialah 0  x  3 Julat f ialah −6  x  4
−1
–1
Range of f is Range of f is
–1
14. Cari fungsi songsang bagi setiap yang berikut. SP 1.3.3 TP4 E-pop Quiz
Find the inverse function of each of the following.
(a) f(x) = 7 – 5x, f (4) 7 – x
−1
−1
f(x) = 4x – 3, f (5) (b) f(x) = 5 , f (3)
−1
Katakan / Let y = 4x − 3 Katakan / Let y = 7 – 5x Katakan / Let y = 7 – x
4x = y + 3 5x = 7 – y 5
y + 3 7 – y 5y = 7 – x
x = x =
4 5 x = 7 – 5y
−1
f (y) = x f (y) = x f (y) = x
−1
−1
y + 3 7 – y
= = = 7 – 5y
4 5
Gantikan y dengan x / Replace y with x Gantikan y dengan x Gantikan y dengan x
Replace y with x
Replace y with x
−1
f (x) = x + 3 7 – x
−1
4 f (x) = 5 f (x) = 7 – 5x
−1
f (5) = 5 + 3 = 2 7 – 4 3 f (3) = 7 – 5(3) = –8
−1
−1
4 f (4) = =
−1
5 5
 
(c) f(x) = 2x + 5 , f (–8) (d) f(x) = x + 2 , f −1 3 (e) f(x) = 2x , f (–3)
−1
−1
x 4x – 2 4 4 – x
Katakan / Let y = 2x + 5 Katakan / Let y = x + 2 Katakan / Let y = 2x
x 4x – 2 4 – x
xy = 2x + 5 4xy – 2y = x + 2 4y – xy = 2x
xy – 2x = 5 4xy – x = 2 + 2y 2x + xy = 4y
x(y – 2) = 5 x(4y – 1) = 2 + 2y x(2 + y) = 4y
x = 5 2 + 2y 4y
y – 2 x = 4y – 1 x = 2 + y
f (y) = x f (y) = x f (y) = x
−1
−1
−1
= 5 2 + 2y 4y
y – 2 = 4y – 1 = 2 + y
Gantikan y dengan x
Replace y with x Gantikan y dengan x Gantikan y dengan x
Replace y with x
Replace y with x
f (x) = 5 2 + 2x −1 4x
−1
−1
x – 2 f (x) = 4x – 1 f (x) = 2 + x
f (–8) = 5 = – 1 3
−1
–8 – 2 2 2 + 2   f (–3) = 4(–3) = 12
−1
4
 
f −1 3 = 4   – 1 = 7 2 – 3
3
4
4
9 4 © Penerbitan Pelangi Sdn. Bhd.
01 Hybrid PBD Mate Tambahan Tg4.indd 9 29/09/2021 3:23 PM