Page 25 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
(IV) If f and g are inverse functions of each other, Solution
then the graph of y = g(x) is the reflection of (a) y
the graph of y = f(x) along the line y = x. 5 y = f(x) y = x

y 4
y = x 3
7 2
6 y = g(x)
1
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5 x
4 –6 –5 –4 –3 –2 –1 –1 0 1 2 3 4 5 6
3
–2
2 –3
y = g(x) 1 –4
x
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –5
–1 y = f(x) –6
–2
Form 4
–3 (b) y
–4 y = x
5
–5 y = g(x)
4
3 y = f(x)
The line y = x is the axis of reflection. 2
1
x
–4 –3 –2 –1 0 1 2 3 4 5
28 –1
–2
Each of the following diagrams shows the graph of –3
y = f(x). Copy and draw the graph of y = g(x) where f –4
and g are inverse functions of each other.
(a)
y
Try Question 9 in ‘Try This! 1.3’
5 y = f(x)
4
3 (V) If a point (a, b) lies on the graph y = f(x), then
2 the point (b, a) lies on the graph y = g(x) where
1 f and g are inverse functions of each other.
x
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
–1 29
–2
–3 The following table shows the points on the graph of
–4 y = f(x) and the corresponding points on the graph of
–5 y = g(x).
–6
Point on the graph of Point on the graph of
(b) y y = f(x) y = g(x)
5
4 (−3, −3) (−3, −3)
3 y = f(x)
2 (−1, 1) (a, −1)
1 (0, b) (3, c)
x
–4 –3 –2 –1 0 1 2 3 4 5
–1 Given f and g are inverse functions of each other.
–2 (a) Determine the values of a, b and c.
–3 (b) Why does the point (−3, −3) on the graph
–4
of y = f(x) remain unchanged on the graph of
y = g(x)?

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