Page 5 - 1202 Question Bank Additional Mathematics Form 4

12. Continuous function is a function where the points
are connected by a straight line or a curve within the f
given interval.
x ● ● y
f(x)
f –1
4
3
If f (x) = y, then f (y) = x
–1
2. Properties of inverse function:
x
0 2 4 (a) A function f that maps set A to set B has an inverse
–1
Domain of f is 0 < x < 4 function f if f is a one-to-one function.
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Codomain of f is 0 < f (x) < 4 (b) fg(x) = x where x in the domain of g and gf (x) = x
Range of f is 0 < f (x) < 4 where x in the domain of f.
(c) If two functions, f and g are inverse to each other,
1.2 Composite Functions then
(i) domain of f = range of g,
1. Composite function: (ii) domain of g = range of f,
(iii) graph g is a reflection of graph f.
f g (d) For any real numbers, a and b, if the point (a, b)
is on the graph f, then the point (b, a) is on the
x
y = f(x) z = g(f(x)) graph g.
3. Horizontal line test:
gf
If the horizontal line intersects the graph of a function
A B C
at only one point, then this type of function is
2. If a function f maps x to y, written as f (x) = y and one-to-one function and it has an inverse function.
another function g maps y to z, written as g(y) = z, f(x)
then gf (x) maps x to z and is written as gf (x) = z. f
3. gf (x) ≠ fg(x)
4. f (x) = fff (x) = ff (x) = f f (x) Horizontal
2
2
3
line test
1.3 Inverse Functions 0 x
1. An inverse function maps an image to its object.

PAPER 1

Section A

1. The diagram shows a relation between set A and Answer:
SPM set B. (a)
CLONE
A B
f
6 ● ● 13
8 ● ● 17

p ● ● q
(b)
State
(a) the function of f (p), [2 marks]
(b) q in terms of p. [3 marks]

2 Question 1(a):
SOS TIP Write f (x) = ax + b, then find a and b. 22

01_1202 QB AMath F4.indd 2 09/05/2022 11:30 AM