Page 11 - PBD Plus Matematik Tambahan T4 (EG)
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Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
(a) Fungsi f ditakrifkan oleh f : x → |3x + 1|.
Function f is defined by f : x → |3x + 1|.
(i) Lakarkan graf bagi f untuk domain –3 x 2 . (iii) Cari domain bagi f(x) 4.
Sketch the graph of f in the domain –3 x 2. Find the domain of f(x) 4.
(ii) Cari nilai bagi f(–4). (iv) Cari domain bagi f(x) 5.
Find the value of f(–4). Find the domain of f(x) 5.
f(x)
(i) x y = f(x) = |3x + 1| 8 (ii) f(–4) = |3(–4) + 1|
–3 8 7 = |–11|
= 11
– 1 0 (iii) f(x) 4
3
0 1 1 3x + 1 –4 , 3x + 1 4
3x 3
3x –5
2 7 x 5
–3 1 0 2 x – x 1
– 3 3
(iv) f(x) 5
|3x + 1| 5
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–5 3x + 1 5
–6 3x 4
–2 x 4
3
Fungsi Gubahan
1.2 Buku Teks ms. 12 – 19
Composite Functions
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. Tip Penting
2. Fungsi f memetakan set B kepada set C. fg(x) diperoleh dengan
Function f maps set B to set C. x g(x) fg(x) menggantikan fungsi g
3. Fungsi yang memetakan set A kepada set C ialah fungsi ke dalam fungsi f.
gubahan, fg. fg(x) = f[g(x)]
The function which maps set A to set C is composite function, fg
fg
SP 1.2.1 Memerihalkan hasil gubahan dua fungsi.
SP 1.2.2 Menentukan fungsi gubahan.
7. Tentukan fungsi gubahan bagi dua fungsi yang diberikan. TP 3
Determine the composite functions of the two functions given.
Contoh
Dua fungsi ditakrifkan oleh f : x → x + 2 dan (a) Dua fungsi ditakrifkan oleh f : x → 2x − 1 dan
g : x → x + 3. g : x → x + 5.
2
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)
= (x + 3) + 2 = f(x + 5) = g(x + 5)
2
2
= x + 5 = 2(x + 5) – 1 = (x + 5) + 5
2
2
2
2
4
2
(ii) gf(x) = g(x + 2) Tip Penting = 2x + 10 – 1 = x + 10x + 25 + 5
2
2
4
= (x + 2) + 3 = 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
2
= 4x – 4x + 6
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