Page 15 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

22. Solve each of the following problems. PL 5
Selesaikan masalah-masalah berikut.
Example

Given the function f : x → 4x – 7 and g : x → x – 5, find
2
Diberi fungsi f : x → 4x – 7 dan g : x → x – 5, cari
2
–1
–1
–1
(i) f (x), (ii) gf (x), (iii) gf (5)
2
(i) Let y = f(x) (ii) gf (x) = g  x + 7  (iii) gf (5) = 5 + 14(5) – 31
–1
–1
y = 4x – 7 4 16
4x = y + 7 2 = 64
y + 7 =  x + 7  – 5 16
x = 4 = 4
4
2
–1
Since f (y) = x, =  x + 14x + 49  – 5
y + 7 16
f (y) = 2
–1
4 = x + 14x + 49 – 80
16
Substitute y with x, x + 14x – 31
2
x + 7 =
f (x) = 16
–1
4
2x + p
(a) Given g : x → , p ≠ 4 and g(4) = 5, find
p – 4
2x + p
Diberi g : x → , p ≠ 4 dan g(4) = 5, cari
p – 4
(i) the value of p / nilai p,
(ii) g (x),
–1
(iii) the value of x if g (x) = 4 / nilai x jika g (x) = 4.
–1
–1
2(4) + p 2x + 7 3x – 7
(i) g(4) = (ii) g(x) = (iii) g (x) =
–1
p – 4 3 2
8 + p Let y = g(x) g (y) = x 3x – 7
–1
5 = 4 = 2
p – 4 y = 2x + 7
5(p – 4) = 8 + p 3 8 = 3x – 7
5p – 20 = 8 + p 3y = 2x + 7 3x = 15
4p = 28 x = 3y – 7 x = 5
p = 7 2
3x – 7
–1
∴ g (x) =
2
5
(b) It is given g : x → 8x – 3 and h : x → x , x ≠ 0. Find
5
Diberi bahawa g : x → 8x – 3 dan h : x → , x ≠ 0. Cari
x
(i) g (x), (ii) hg (x), (iii) g h(10).
–1
–1
–1
(i) Let y = g(x) (ii) hg (x) = h  x + 3  (iii) h(10) = 5 = 1
–1
y = 8x – 3 8 10 2
8x = y + 3 5
1
y + 3 = –1 –1  
x = x + 3 g h(10) = g 2
8
8 1
Since g (y) = x, 40 2 + 3
–1
y + 3 = =
g (y) = x + 3 8
–1
8 7
=
Substitute y with x, 16
x + 3
g (x) =
–1
8
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