Page 10 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

14. Solve the following problems. PL 4
Selesaikan masalah-masalah berikut.
Example

Given the functions f : x → 4x – 1 and g : x → (x – 3) . Find
2
2
Diberi fungsi f : x → 4x – 1 dan g : x → (x – 3) . Cari
(i) fg(x), (ii) fg(3).
2
(i) fg(x) = f[(x – 3) ] (ii) fg(3) = 4(3) – 24(3) + 35
2
2
= 4(x – 3) – 1 = 36 – 72 + 35
= 4(x – 6x + 9) – 1 = –1
2
= 4x – 24x + 36 – 1
2
= 4x – 24x + 35
2
(a) Given f : x → 3x + 8 and g : x → x – 6. Find
Diberi f : x → 3x + 8 dan g : x → x – 6. Cari
(i) fg(x), (ii) fg(–2).
(i) fg(x) = f(x – 6) (ii) fg(–2) = 3(–2) – 10
= 3(x – 6) + 8 = –16
= 3x – 18 + 8
= 3x – 10

(b) A function g is defined by g : x → x + 2. Find the function f for each of the following composite functions.
Fungsi g ditakrifkan oleh g : x → x + 2. Cari fungsi f bagi setiap fungsi gubahan berikut.
(i) fg : x → x + 4x + 4, (ii) gf : x → 2x – 3x + 4.
2
2
2
(i) fg(x) = x + 4x + 4 (ii) gf(x) = 2x – 3x + 4
2
2
f(x + 2) = x + 4x + 4 f(x) + 2 = 2x – 3x + 4
2
2
f(x) = 2x – 3x + 2
Let y = x + 2
x = y – 2
2
So, f(y) = (y – 2) + 4(y – 2) + 4
2
= y – 4y + 4 + 4y – 8 + 4
= y 2
∴ f(x) = x 2
(c) Given f(x) = px + q and f (x) = 4x + 6. Find the values of p and q.
2
Diberi f(x) = px + q dan f (x) = 4x + 6. Cari nilai-nilai p dan q.
2
ff(x) = 4x + 6 Comparing: When p = 2, When p = –2,
f(px + q) = 4x + 6 p = 4 pq + q = 6 pq + q = 6
2
p(px + q) + q = 4x + 6 p = ±√4 2q + q = 6 –2q + q = 6
p x + pq + q = 4x + 6 = 2 or –2 3q = 6 –q = 6
2
q = 2 q = –6

3x
(d) Functions g and h are defined as g : x → 5x – 6 and h : x → . Find the value of x if gh(x) = h(x).
x – 2
3x
Fungsi g dan h ditakrifkan oleh g : x → 5x – 6 dan h : x → . Cari nilai x jika gh(x) = h(x).
x – 2
g(x) = 5x – 6 3x 3x
3x 5   – 6 = x – 2
h(x) = x – 2
x – 2 3x
15x – 6 =
gh(x) = h(x) x – 2 x – 2
3x
3x
g  x – 2  = x – 2 15x – 6(x – 2) = 3x
15x – 6x + 12 = 3x
6x = –12
x = –2

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