Page 9 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

Example 4

1 Given that the function f : x ↦ 2x + 1, find the function g if
(a) the composite function f g is f g : x ↦ 6x + 11,
°
°
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(b) the composite function g f is g f : x ↦ x – 1 , x ≠ 1.
°
°
Solution: (a) Given that f(x) = 2x + 1.
If f g(x) = 6x + 11.
°
f[g(x)] = 6x + 11.
∴ 2g(x) + 1 = 6x + 11
2g(x) = 6x + 10
g(x) = 3x + 5
Hence, g : x ↦ 3x + 5

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(b) If g f(x) = x – 1 .
°
g[f(x)] = 1 .
x – 1
∴ g(2x + 1) = 1
x – 1
Let u = 2x + 1
then x = 1 (u – 1)
2
Hence, g(u) = 1
1 (u – 1) – 1
2
= 2
u – 3

i.e. g : u ↦ 2 , u ≠ 3 or g : x ↦ 2 , x ≠ 3.
u – 3 x – 3

Exercise 1.1

1. If f(x) = x – 9, x  R, find
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(a) f(0), (b) f(4), (c) f(3), (d) f(–3).
2. Given that f(x) = x + 1 , x  –1,
(a) find the value of
(i) f(8), (ii) f(0), (iii) f(–1),
(b) find the value of x such that
(i) f(x) = 5, (ii) f(x) = 10.
3. By drawing a suitable sketch graph, find the range of each of the following functions.
(a) f(x) = 2x, x  [–1, 3],
(b) f(x) = 2 – x, x  [–1, 3],
(c) f(x) = x – x – 2, x  [–2, 3].
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01a STPM Math T T1.indd 6 3/28/18 4:20 PM