Page 18 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions

g f 14
x y y z
0 0 0 5 Fill in the empty boxes in each of the following arrow
1 2 2 7 diagrams.
2 4 4 9 (a)
3 6 6 11 f g
Set X Set Y Set Y Set Z x
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x z
0 5
1 7 Form 4
2 9 (b)
g f
3 11
Set X Set Z x
2. Note that the two functions involved in obtaining
output z are the combination of function g and f
as follows:
g : x → 2x ‘multiply by 2’ function
f : x → x + 5 ‘add 5’ function Solution

3. The outcome of the combined functions g and (a)
f can be represented by the composite function f g
fg(x), that is fg : x → 2x + 5. The function fg is x gf(x)
known as a composite function. f(x)
4. The composite function can directly give output
values as long as input values are given.
gf
SPM Tips
(b)
(a)
g f g f
x fg(x)
g(x)
x g(x) fg(x)

fg
fg
fg(x) means that the function g acts on x first, then Try Questions 1 – 2 in ‘Try This! 1.2’
only the function f acts on the outcome of function g.
(b) f g
B Determining the composite functions

x f(x) gf(x)
15
2
Given the functions f : x → x and g : x → 2x + 3.
Determine the composite functions for
gf
gf(x) means that the function f acts on x first, (a) fg, (b) gf,
then only the function g acts on the outcome of (c) f , (d) g .
2
2
function f.
15

01 Focus SPM Add Maths F4.indd 15 08/11/2021 1:58 PM