Page 16 - PBD Plus Matematik Tambahan T4 (EG)

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
SP 1.3.3 Menentukan fungsi songsang.

14. Cari fungsi songsang bagi setiap yang berikut. TP 4
Find the inverse function of each of the following.
Contoh
−1
f(x) = 4x – 3, f (5) (a) f(x) = 7 – 5x, f (4) (b) f(x) = 7 – x , f (3)
−1
−1
5
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
f (x) = x + 3 7 – x
−1
4 f (x) = 5 f (x) = 7 – 5x
−1
−1
f (5) = 5 + 3 = 2 7 – 4 3 f (3) = 7 – 5(3) = –8
−1
−1
−1
4 f (4) = =
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 Penerbitan Pelangi Sdn. Bhd. −1
−1
f (y) = x
f (y) = x
−1
= 5 2 + 2y 4y
y – 2 = 4y – 1 = 2 + y
Gantikan y dengan x Gantikan y dengan x
Replace y with 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
Cuba jawab Praktis SPM 1, K2: S6(a) 4
15. Lakukan aktiviti yang berikut. TP 6
Carry out the following activity.
AKTIVITI PAK-21 Stesen
(a) Bahagikan murid kepada 5 kumpulan.
Divide the pupils into 5 groups. Aktiviti
Activity
(b) Imbas kod QR untuk mendapatkan aktiviti.
Scan the QR code to obtain the activity.
(c) Setiap kumpulan bergerak ke setiap stesen dan tuliskan jawapan kumpulan masing-masing pada
sehelai kertas di stesen itu.
Each group moves to each station and write the answer on a piece of paper in the station.
(d) Selepas semua kumpulan selesai menjawab, setiap kumpulan mewakili satu stesen dan semak
jawapan kumpulan lain. Lakukan perbincangan dalam kumpulan bagi menyemak jawapan yang
betul. Guru berikan bimbingan apabila diperlukan.
After all groups finish answering, each group represents a station and check the answers of other groups. Discuss in the group
to check the correct answers. Teacher gives guidance when needed.

TAHAP PENGUASAAN 1 2 3 4 5 6 9 © Penerbitan Pelangi Sdn. Bhd.