Page 10 - Modul A+1 Matematik Tambahan Tingkatan 4

(d) Dalam rajah di bawah, suatu fungsi v memetakan x (e) Diberi f (x) = x – 2 , x ≠ 3 dan g(x) = 3 , x ≠ 2, cari
kepada y dan fungsi w memetakan y kepada z. x – 3 x – 2
In the diagram below, a function v maps x to y and a f (6) dan gf (6).
2
2
function w maps y to z. Given f (x) = x – 2 , x ≠ 3 and g(x) = 3 , x ≠ 2, find f (6) BAB 1
2
x – 3 x – 2
x y z and gf (6).
2
9
v w
2
8 k f (6) = ff (6)
= f  6 – 2 
6 – 3
4
= f  
3
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Diberi v(x) = 1 + x dan w(x) = x – 1, cari 4
2
Given v(x) = 1 + x and w(x) = x – 1, find = 3 – 2
2
(i) nilai k, 4 – 3
the value of k, 3
(ii) fungsi yang memetakan x kepada z. – 2
the function that maps x to z. = 3
– 5
3
(i) k = 9 – 1 = 80 = 2
2
5
2
(ii) wv(x) = w(1 + x) gf (6) = g  
2
5
2
= (1 + x) – 1 3 7
2
= 1 + 2x + x – 1 = 2 = –1 8
2
= 2x + x 5 – 2
2. Selesaikan setiap yang berikut.
Solve each of the following. TP 3
5
Contoh/Example (a) Diberi f : x → x + 6 dan (b) Diberi fungsi m : x → , x ≠ 0
gf : x → x – x + 1, cari fungsi x
2
Diberi f : x → x + 1 dan g(x). dan nm : x → 10x, cari
fg : x → 2x + x – 1, cari fungsi g(x). Given f : x → x + 6 and Given the function m : x → , x ≠ 0
5
2
Given f : x → x + 1 and gf : x → x – x + 1, find the function x
2
fg : x → 2x + x – 1, find the function g(x). and nm : x → 10x, find
2
g(x). (i) n(x),
(ii) nilai x apabila mn(x) = 12.
g[f (x)] = x – x + 1 the value of x when mn(x) = 12.
2
f [g(x)] = 2x + x – 1 g[x + 6] = x – x + 1
2
2
g(x) + 1 = 2x + x – 1 (i) n[m(x)] = 10x
2
5
g(x) = 2x + x – 1 – 1 Katakan x + 6 = y n   = 10x
2
g(x) = 2x + x – 2 x = y – 6 x
2
Gantikan Katakan 5 = y
x
g(y) = (y – 6) – (y – 6) + 1 x = 5
2
g(y) = y – 12y + 36 – y + 6 + 1 y
2
g(y) = y – 13y + 43 Gantikan
2
g(x) = x – 13x + 43 5
2
n(y) = 10  
y
n[y] = 50
y
n(x) = 50
x
(ii) mn(x) = 12
5 = 12
50
 
x
5 ÷ 50 = 12
x
5 × x = 12
50
x = 120
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01_Modul A+ MateTam Tg4.indd 7 08/10/2021 11:18 AM