Analysis and Approaches for IBDP Maths Ebook 2 | Page 21

Exercise 3
1
1. The function f and g are defined as
4x
�1
f( x)
� and
x
g( x) 4
x � .
2
� x , x� , 0
(a) Find the expression of ( f g)( x ).
(b) Show that ( f g)( x ) is an odd function.
It is given that the coordinates of the minimum point of y � ( f g)( x)
are (0.25, 4) .
(c) Write down the range of ( f g)( x ).
[2]
[2]
[1]
2. The function f is defined as
f ( x)
x x
4 2
� � , x� .
(a) Show that f( x ) is an even function.
The minimum point of f has x -coordinate
(b) Find the range of f( x ).
1
� for x � 0 .
2
[2]
[3]
x
3. The function f is defined as f( x)
� , x� .
2
x � 0.19
(a) Show that f( x ) is an odd function.
It is given that f ( a)
� a , a� .
[2]
(b) Find the possible values of a .
(c) Write down the equation of the horizontal asymptote of f( x ).
[3]
[1]
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