Page 16 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

2
(c) Given the function h(x) = ax + b, where a . 0, a and b are constants and h (x) = 49x – 40, find
2
Diberi fungsi h(x) = ax + b, dengan keadaan a . 0, a dan b ialah pemalar dan h (x) = 49x – 40, cari
(i) the value of a and of b, / nilai a dan b,
(ii) h (–3),
–1
–1 2
–1 2
(iii) the value of x if (h ) (x) = 1 / nilai x jika (h ) (x) = 1.
–1 2
(i) Given h(x) = ax + b (ii) h(x) = 7x – 5 (iii) (h ) (x) = 1
h (x) = hh(x) Let y = h(x) x + 5
2
= h(ax + b) y = 7x – 5 7 + 5
= a(ax + b) + b 7x = y + 5 7 = 1
= a x + ab + b y + 5
2
x = 7 x + 5 + 5 = 7
Compare with 49x – 40, 7
–1
2
a = 49 Since h (y) = x, x + 5 = 2

a = 49 h (y) = y + 5 7
–1
= 7 7 x + 5 = 14
x = 9
Substitute y with x,
ab + b = –40 –1 x + 5
7b + b = –40 h (x) = 7
8b = –40 –3 + 5
–1
b = –5 ∴ h (–3) =
7
2
=
7
3x – 6 mx + 6
–1
(d) It is given that f (x) = and f (x) = . Find HOTS Analysing
7 + 4x 3 + nx
3x – 6 mx + 6
–1
Diberi bahawa f (x) = dan f (x) = . Cari
7 + 4x 3 + nx
(i) the values of m and n, / nilai m dan n,
(ii) the value of x if f(4x + 3) = 7. / nilai x jika f(4x + 3) = 7.
3x – 6 7x + 6
(i) f (x) = (ii) f(4x + 3) = 7, f(x) =
–1
7 + 4x 3 – 4x
Let y = f (x) 7 = 7(4x + 3) + 6
–1
3x – 6 3 – 4(4x + 3)
y =
7 + 4x 28x + 21 + 6
7y + 4xy = 3x – 6 7 = 3 – 16x – 12
7y + 6 = 3x – 4xy 28x + 27
7y + 6 = x(3 – 4y) 7 = –9 – 16x
7y + 6
x = 7(–9 – 16x) = 28x + 27
3 – 4y
–63 – 112x = 28x + 27
Since f(y) = x, –140x = 90
7y + 6 9
f(y) = x = –
3 – 4y 14
Substitute y with x,
7x + 6
f(x) =
3 – 4x
Compare with
mx + 6
f (x) =
3 + nx
7x + 6 = mx + 6
3 – 4x 3 + nx
∴ m = 7, n = –4

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