Page 12 - PBD Plus Matematik Tambahan T4 (EG)

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
SP 1.2.3 Menentukan imej suatu fungsi gubahan apabila objek diberi dan sebaliknya.
x – 1 1
8. Diberi dua fungsi f : x → dan g : x → . TP 3
2 x
x – 1 1
Given the two functions f : x → and g : x → .
2 x
Contoh
(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
2
Find the value of x when g (x) = 5. 2
(i) fg(x) (ii) gg(x) (i) gf(x) = g  x – 1  (iii) ff(x) = f  x – 1 
1
1
2
= f   = g   1 2 x – 1
x
x
1 – 1 = 1 = x – 1 = 2 – 1
2
= x 2 1 = 2 = x – 1 – 2
2
x
Penerbitan Pelangi Sdn. Bhd.
= 1 – x , x ≠ 0 = x x – 1 4
2x gg(x) = 5 ∴ gf(–1) = 2 = x – 3
∴ 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
SP 1.2.4 Menentukan suatu fungsi berkaitan apabila fungsi gubahan dan salah satu fungsinya diberi.
9. Nyatakan fungsi f bagi setiap yang berikut berdasarkan fungsi g dan fungsi gubahan yang diberikan. TP 4
State the function f of each of the following based on the given function g and the composite function.
Contoh
(i) g(x) = x − 6 dan / and gf(x) = x − 3. (ii) g(x) = x + 5 dan / and fg(x) = 2x + 15.

gf(x) = x – 3 Katakan / Let y = g(x)
f(x) – 6 = x – 3 y = x + 5
f(x) = x + 3 x = y – 5
fg(x) = 2x + 15
f(y) = 2(y – 5) + 15
= 2y – 10 + 15
= 2y + 5
f(x) = 2x + 5

(a) g(x) = x + 9 dan / and gf(x) = x − 7. (b) g(x) = 2x – 5 dan / and fg(x) = 2x + 1.

gf(x) = x – 7 Katakan / Let fg(x) = 2x + 1
f(x) + 9 = x – 7 y = g(x) f(y) = 2  y + 5  + 1
f(x) = x – 16 y = 2x – 5 2
x = y + 5 = y + 6
2 f(x) = x + 6

(c) g(x) = 5x + 7 dan / and gf(x) = 3x − 1. (d) g(x) = 3x + 1 dan / and fg(x) = 3x + 2.
gf(x) = 3x – 1 Katakan / Let fg(x) = 3x + 2
5[ f(x)] + 7 = 3x – 1 y = g(x) f(y) = 3  y – 1  + 2
f(x) = 3x – 8 y = 3x + 1 3
5 x = y – 1 = y + 1
3 f(x) = x + 1

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