Page 5 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

4. State the domain, codomain and range for each of the following. PL 2
Nyatakan domain, kodomain dan julat bagi setiap yang berikut.
Example
(ii)
(i) f(x) f(x)
19
8
6
4 x
2 –2 0 2 3
–8
x
–4 –3 –2 –1 0 1 2 3 –16
The domain of f is –2 < x < 3.
Domain = {–4, –2, –1, 2, 3} The codomain of f is –16 < f(x) < 19.
Codomain = {2, 4, 6, 8} The range of f is –16 < f(x) < 19.
Range = {2, 4, 6, 8}

(a) f(x) (b) f(x)
8 4
6 3
4
2
x
0 x
–4 –3 –2 –1 1 2 3 0 1 3

Domain = {–4, –2, 0, 2, 3} The domain of f is 0 < x < 3.
Codomain = {0, 2, 4, 8} The codomain of f is 0 < f(x) < 4.
The range of f is 0 < f(x) < 4.
Range = {0, 2, 4, 8}

5. For each of the following functions, find the image for the object x given. PL 3
Untuk setiap fungsi berikut, cari imej bagi objek x yang diberikan.
Example (a) f(x) = 3x + 7; x = –4, x = 5 (b) f(x) = x + 1; x = 3, x = –2
2
f(x) = 9x – 4; x = 2, x = –1
f(–4) = 3(–4) + 7 f(3) = (3) + 1
2
= –5 = 10
f(2) = 9(2) – 4 f(5) = 3(5) + 7 f(–2) = (–2) + 1
2
= 14 = 22 = 5
f(–1) = 9(–1) – 4
= –13

6. For each of the following functions, find the object x based on the image given. PL 3
Untuk setiap fungsi berikut, cari objek x bagi imej yang diberikan.

Example (a) f(x) = 5x + 7; f(x) = –1, f(x) = –3 (b) f(x) = x + 5; f(x) = 9, f(x) = 21
2
f(x) = 2x – 1; f(x) = 3, f(x) = 5
5x + 7 = –1 x + 5 = 9
2
5x = –8 x = 4
2
2x – 1 = 3 8 x = 2 or –2
2x = 4 x = – 5
x = 2 2
5x + 7 = –3 x + 5 = 21
2
2x – 1 = 5 5x = –10 x = 16
x = 4 or –4
2x = 6 x = –2
x = 3

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