Page 30 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
15. The following diagram shows a graph of function 16. A function f is defined by f(x) = x + 5.
y = f(x), such that f(x) = (x – 1) – 3. (a) Find the inverse function, f .
2
–1
y (b) Hence, verify that the composite functions
f [f (x)] and f [f(x)] are equal to the identity
–1
–1
2 function.
1
x
–1 0 1 2 3 4
–1
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–2
–3
Find f (x) and state a suitable domain.
–1
SPM Practice 1 Form 4
SPM Practice

PAPER 1 (a)
1. Fahmi works at the marketing department of a y
perfume company. He intends to introduce a type of
perfume which is filled in a conical bottle where the
ratio of the height of the cone to the radius of the 1
cone is 5 : 1 as shown in the following diagram.
0.5

x
0 20° 40° 60° 80° 100° 120° 140° 160° 180°

h (b)
y

2
1
r x
–4 –3 –2 –1 0 1 2 3 4
By using function notation, write the volume of the
conical bottle
(a) as a function of the radius, r.
(b) as a function of the height, h. 4. The diagram below shows the graph of function
f(x) = |2x + 3| for the domain – 4 < x < 0.
2. A function t maps the temperature, in degrees
Celsius, to the temperature in degrees Farenheit. y
The function t is defined as t : C → 9C + 32, y = f(x)
5
C  R. Find h
(a) t(–10),
(b) the value of C when t(C) = C.
–4 k 0 x
3. Complete the following table based on the given
function.
State
Function Domain Range (a) the values of h and k.
(b) the range of f(x) that corresponds to the given
(a) y = sin x 0° < x < 180° domain.
1
(b) y = x  R
x + 1
2

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