Page 8 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

y

f 1
g

x z
g f
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Figure 1.4
For example, if
f : x ↦ x – 2 and g : x ↦ 3x,
i.e. f(x) = x – 2 and g(x) = 3x,
then g[f(x)] = 3f(x)
= 3(x – 2)
Hence, g f : x ↦ 3(x – 2)
°
For example, if x = 5,
f(5) = 5 – 2 = 3
g(3) = 3(3) = 9
i.e. g[f(5)] = g(3) = 9

3

f
g

5 9
g f
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Figure 1.5

Example 3

2
If f(x) = x and g(x) = x + 1, find
(a) f g(x) (b) g f(x)
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°
(c) f f(x) (d) g g(x)
°
°
Solution: (a) f g(x) = f[g(x)] (b) g f(x) = g[f(x)]
°
°
2
= f(x + 1) = g(x )
= (x + 1) 2 = x + 1
2
(c) f f(x) = f[f(x)] (d) g g(x) = g[g(x)]
°
°
= f(x ) = g(x + 1)
2
= (x ) = (x + 1) + 1
2 2
= x 4 = x + 2
Note: 1. f g ≠ g f, from (a) and (b).
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°
2. f[g(x)] ≠ f(x) · g(x) since f[g(x)] = (x + 1) whereas f(x) · g(x) = x (x + 1).
2
2
5

01a STPM Math T T1.indd 5 3/28/18 4:20 PM