Page 23 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi

PBD 1.2 Fungsi Gubahan Buku Teks
PBD
PBD
Composite Functions ms. 12 – 19
FOKUS TOPIK

1. Fungsi g memetakan set A kepada set B. Set A g Set B f Set C
Function g maps set A to set B.
2. Fungsi f memetakan set B kepada set C.
Function f maps set B to set C.
x g(x) fg(x)
3. Fungsi yang memetakan set A kepada set C ialah fungsi gubahan, fg.
The function which maps set A to set C is composite function, fg

(i) fg(x) Penerbitan Pelangi Sdn Bhd. All Rights Reserved
fg
7. Tentukan fungsi gubahan bagi dua fungsi yang diberikan. SP 1.2.1 SP 1.2.2 TP3
Determine the composite functions of the two functions given.

Dua fungsi ditakrifkan oleh f : x → x + 2 dan (a) Dua fungsi ditakrifkan oleh f : x → 2x − 1 dan
2
g : x → x + 3. g : x → x + 5.
Two functions are defined by f : x → x + 2 and g : x → x + 3. Two functions are defined by f : x → 2x − 1 and g : x → x + 5.
2
(i) fg (ii) gf (iii) f 2 (i) fg (ii) gf (iii) g 2
(i) fg(x) = f(x + 3) (i) fg(x) (iii) gg(x)
2
2
= (x + 3) + 2 = f(x + 5) = g(x + 5)
= x + 5 = 2(x + 5) – 1 = (x + 5) + 5
2
2
2
= 2x + 10 – 1 = x + 10x + 25 + 5
2
4
2
(ii) gf(x) = g(x + 2) 2 4 2
= (x + 2) + 3 Tip Penting = 2x + 9 = x + 10x + 30
= x + 5 fg(x) = f[g(x)] (ii) gf(x)
f (x) = ff(x)
2
(iii) ff(x) = f(x + 2) = g(2x – 1)
2
= (x + 2) + 2 = (2x – 1) + 5
2
= x + 4 = 4x – 4x + 1 + 5
= 4x – 4x + 6
2
x – 1 1
8. Diberi dua fungsi f : x → dan g : x → . SP 1.2.3 TP3
2 x
x – 1 1
Given the two functions f : x → and g : x → .
2 x
(a) (i) Cari gf(–1). / Find gf(–1).
(i) Cari fg(2). 1
2
Find fg(2). (ii) Cari nilai x apabila f (x) = .
2
1
(ii) Cari nilai x apabila g (x) = 5. Find the value of x when f (x) = .
2
2
Find the value of x when g (x) = 5. 2
2
(ii) gg(x) (i) gf(x) = g  x – 1  (iii) ff(x) = f  x – 1 
2
1
1
= f   = g   1 2 x – 1 – 1
x
x
1 – 1 = 1 = x – 1 = 2
2
= x 2 1 = 2 = x – 1 – 2
x
2
4
= 1 – x , x ≠ 0 = x x – 1 x – 3
2x gg(x) = 5 ∴ gf(–1) = 2 =
∴ fg(2) = 1 – 2 x = 5 –1 – 1 4
1
2(2) = –1 ff(x) =
2
= – 1 x – 3 1
4 =
4 2
x = 5
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