Page 9 - Modul A+1 Matematik Tambahan Tingkatan 4

1.2 Fungsi Gubahan m.s. 12-19
Buku Teks
Composite Functions
BAB 1 1. Selesaikan setiap yang berikut.

Solve each of the following. TP 3

Contoh/Example (a) Fungsi f dan fungsi g masing-masing ditakrifkan oleh
f : x → 2x – 5 dan g : x → –11 + 8x. Cari ungkapan
2
Dalam gambar rajah anak panah di bawah, fungsi f bagi fg dan gf. Seterusnya, cari nilai-nilai x apabila
memetakan set M kepada set N manakala fungsi g Functions f and g are defined by f : x → 2x – 5 and
2
memetakan set N kepada set P. g : x → –11 + 8x respectively. Find the expression of fg and
In the arrow diagram below, function f maps set M to set N gf. Hence, find the values of x when
whereas function g maps set N to set P. (i) f = g
(ii) fg = 3gf + 6
f g
x x + 2 3x 2
fg(x) = f(–11 + 8x) = 2(–11 + 8x) – 5
2
gf (x) = g(2x – 5) = –11 + 8(2x – 5) = 16x – 51
2
2
2
Set M Set N Set P
2
Dengan menggunakan tatatanda fungsi, nyatakan (i) 2x – 5 = –11 + 8x
2
By usingn the function notation, state 2x – 8x + 6 = 0
(i) fungsi f, (ii) fungsi g, x = 3 atau x = 1
the function f, the function g,
2
2
(iii) fungsi f , (iv) fungsi gf . (ii) 2(–11 + 8x) – 5 = 3(16x – 51) + 6
2
2
2
2
the function f , the function gf . 2(64x – 176x + 121) – 5 – 3(16x )
2
2
+ 3(51) – 6 = 0
128x – 352x + 242 – 5 – 48x + 153 – 6 = 0
2
2
(i) f (x) = x + 2 80x – 352x + 384 = 0
2
(ii) gf (x) = 3x 2 x = 2.4 atau x = 2
g(x + 2) = 3x 2
Katakan/Let x + 2 = y
x = y – 2
g(y) = 3(y – 2) 2
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∴ g(x) = 3(x – 2)
2
(iii) f (x) = f (x + 2) = (x + 2) + 2 = x + 4
2
(iv) gf (x) = g(x + 4) = 3(x + 4 – 2)
2
2
= 3(x + 2) 2
(b) Diberi h : x → px + q dan h : x → 9x + 8. (c) Diberi f (x) = 3m – 7x dan g(x) = 2n + 3x dengan
2
Cari nilai bagi p + 2q jika p > 0. keadaan f = gf. Ungkapkan x dalam sebutan m dan n.
2
Given h : x → px + q and h : x → 9x + 8. Given f (x) = 3m – 7x and g(x) = 2n + 3x such that f = gf.
2
2
Find the value of p + 2q if p > 0. Express x in terms of m and n.
hh(x) = p(px + q) + q
hh(x) = p x + pq + q ff (x) = 3m – 7(3m – 7x)
2
= 3m – 21m + 49x
Bandingkan dengan h (x) = 9x + 8 = –18m + 49x
2
2
p = 9 gf (x) = 2n + 3(3m – 7x)
2
2 p = 3 (sebab p > 0) = 2n + 9m – 21x
3q + q = 8 –18m + 49x = 2n + 9m – 21x
4q = 8 49x + 21x = 2n + 9m + 18m
q = 2 70x = 2n + 27m
x = 2n + 27m
p + 2q = 3 + 2(2) = 7 70

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