Page 13 - Modul A+1 Matematik Tambahan Tingkatan 4

1.3 Fungsi Songsang m.s. 20-30
Buku Teks
Inverse Functions
BAB 1 x – 5
1. Suatu fungsi ditakrifkan sebagai f (x) =
3 . Tentukan setiap yang berikut.
A function is defined as f (x) = x – 5 . Determine each of the following. TP 2
3
–1
Contoh/Example (a) f (–1)
f (3) Katakan a = f (–1)
–1
f (a) = –1 a = 2
a – 5 ∴ f (–1) = a = 2
–1
3 – 5 2 = −1
3
–1©PAN ASIA PUBLICATIONS
f (3) = 3 = – 3 a – 5 = –3
(b) Imej bagi 6 di bawah f. (c) Objek bagi 1.
The image of 6 under f. The object of 1.

f (6) = 6 – 5 = 1 x – 5 = 1 x – 5 = 3
3
3 3 x = 8

2. Tentukan sama ada setiap fungsi berikut mempunyai fungsi songsang atau tidak. Berikan justifikasi anda.
Determine whether each of the following functions has an inverse function or not. Give your justification TP 2

Contoh/Example (a) (b) {(1, 3), (4, 2), (5, 7), (2, 8)}
f(x)
f
x f(x) 3 Ya. f mempunyai satu imej.
–1
–2 1
2 6 0 3 x
4 13 f (x) = 3 – x

Set A Set B Ya. f mempunyai satu imej.
–1
Tidak. f mempunyai dua imej.
–1
No. f has two images.
–1

3. Selesaikan setiap yang berikut.
Solve each of the following. TP 5

Contoh/Example
x + 3
Tentukan sama ada fungsi h : x → 4x – 3 dan g : x → 4 adalah songsang antara satu sama lain.
x + 3
Determine whether the functions h : x → 4x – 3 and g : x → are inverse to each other.
4
(Kaedah 1/Procedure 1) (Kaedah 2/Procedure 2)
h : x → 4x – 3 x + 3
Katakan/Let 4x – 3 = y hg(x) = h  4  gh(x) = g(4x – 3)
(4x – 3) + 3
x = y + 3 = 4  x + 3  – 3 = 4
4
4
h (x) = x + 3 = x + 3 – 3 = 4x
4
4
x + 3 = x = x
g : x → 4 Maka, h(x) dan g(x) adalah songsang antara satu sama lain.
Katakan/Let x + 3 = y Hence, h(x) and g(x) are inverse to each other.
4
x = 4y –3
–1
g (x) = 4x – 3
Maka, h(x) dan g(x) adalah songsang antara satu sama lain.
Hence, h(x) and g(x) are inverse to each other.

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