Page 31 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
5. The functions g and h are defined as PAPER 2
x
2
g(x) = – 1 and h(x) = x – x
2 1. The functions f and g are defined as
respectively. 2x
x + 1
(a) Find g (x). f(x) = x + 1 , x > 0 and g(x) = ABBBB, x . −1
–1
–1
(b) Solve for gh(x) = g (x).
respectively.
6. The following diagrams show four different graphs.
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In each case, the entire graph is shown and the (a) Find fg(8).
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scale on both axes are the same. (b) Write an expression for f (x). Give your answer
ax
A y in the form of bx + c , where a, b and c are
constants.
(c) Write an expression for g (x). Hence, state its
–1
x
O domain and range.
(d) The following diagram shows the graph of
Form 4
y = g(x).
B y
y
7
x
O 6
5
4
3
C y 2 y = g(x)
1
x
–1 0 1 2 3 4 5 6 7 8 9
x
O
On the same axes, sketch the graph of
D y y = g (x).
−1
2. In the Beijing 2008 Olympics, Usain Bolt, or also
x known as ‘Lightning Bolt’, had set a world record
O
in a 100 m race at 9.69 seconds. However, in the
last 20 m of the race, Bolt was seen looking around,
and after knowing that he was leading the other
In the table below, mark ✓ for the correct relation for racers by quite a distance, Bolt slowed down and
each graph, if any. started celebrating his victory. His coach claimed
that if Bolt maintained his speed for the entire race,
A B C D he could have recorded a better run time of 9.52
Not a function seconds. A group of physicists, led by Hans Kristian
Eriksen, have investigated the claim. They found
One-to-one function that in most of Bolt’s races, his position, in m, can be
A function which is its own represented by a function s(t) = 11.8t – 12.5, where t
inverse is the time, in seconds.
A function which does not have (a) Suggest one reason why the domain of this
function need not necessarily begin at t = 0.
an inverse (b) Determine the inverse function of s(t).
(c) What is represented by the inverse function in
7. The functions f and g are defined as f : x → x – 3 (b)?
and g : x → x respectively. Find (d) Use the inverse function in (b) to determine
2
(a) gf(x), whether the claim by Bolt’s coach was true.
2
(b) h(x) such that hgf(x) = x – 6x + 3.

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