Page 13 - PBD Plus Matematik Tambahan T4 (EG)

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi

SP 1.2.5 Menyelesaikan masalah yang melibatkan fungsi gubahan.
10. Selesaikan setiap yang berikut.
Solve each of the following.

(a) Diberi fungsi f(x) = 7 – 2x, g(x) = ax + b dan fg(x) = 1 – 4x, cari nilai a dan nilai b. TP 3
Given the function f(x) = 7 – 2x, g(x) = ax + b and fg(x) = 1 – 4x, find the value of a and of b.
fg(x) = f(ax + b)
= 7 – 2(ax + b)
= 7 – 2ax – 2b

Secara perbandingan / By comparison
7 – 2b – 2ax = 1 – 4x

7 – 2b = 1 , –2a = –4
b = 3 a = 2

(b) Fungsi f ditakrifkan oleh / Function f is defined by
f : x → x , x ≠ –1. TP 4
x + 1
4
3
2
(i) Ungkapkan f (x), f (x) dan f (x) dalam bentuk termudah.
Express f (x), f (x) and f (x) in the simplest form.
4
2
3
(ii) Kemudian, deduksikan f (x).
5
5
Hence, deduce f (x).
(i) f (x) = f [f(x)] f (x) = f [f (x)] f (x) = f [f (x)]
3
3
2
2
4
x x x
= x + 1 = 2x + 1 = 3x + 1
x + 1 x + 1 x + 1
x + 1 Penerbitan Pelangi Sdn. Bhd. 3x + 1
2x + 1
= x = x = x
2x + 1 3x + 1 4x + 1
(ii) Pengangka sentiasa x dan penyebut ialah 2x + 1, 3x + 1 dan 4x + 1, maka penyebut seterusnya ialah
5x + 1 .
The numerator is always x and the denominators are 2x + 1, 3x + 1 and 4x + 1, thus the next denominator is 5x + 1.
x
∴ f (x) =
5
5x + 1
(c) Seorang jurujual akan menerima komisen sebanyak 8% jika jumlah jualannya, RMx melebihi RM4 000
setiap bulan. Diberi dua fungsi f(x) = 0.08x dan g(x) = x – 4 000, antara fg(x) dan gf(x), fungsi gubahan
yang manakah menentukan jumlah komisen yang akan diterima oleh jurujual itu setiap bulan?
A salesperson will receive commission of 8% if his total sales, RMx exceeds RM4 000 every month. Given two functions f(x) = 0.08x
and g(x) = x – 4 000, which composite function, fg(x) and gf(x) will determine the total commission received by the salesperson every
month? TP 5 KBAT Menganalisis
fg(x) = f(x – 4 000) Katakan jumlah jualan, x = RM7 000
= 0.08(x – 4 000) Let the total sales, x = RM7 000
= 0.08x – 320 Jumlah komisen / Total commission
fg(7 000) = 0.08(7 000) – 320 = RM240
gf(x) = g(0.08x) gf(7 000) = 0.08(7 000) – 4 000 = –RM3 440
= 0.08x – 4 000
Maka, fungsi jumlah komisen ialah fg(x).
Thus, the function of the total commission is fg(x).

Cuba jawab Praktis SPM 1, K1: S7

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