Analysis and Approaches for IBDP Maths Ebook 1 | Page 46

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 13
3
1. Let f ( x) � log 5
x , for x � 0 .
(a)
(b)
Let
Show that f
( x) � 5 x .
�1 3
Write down the range of
g( x) log 5
x
x � .
2
� , for 0
1
f � .
[2]
[1]
(c)
2. Let
f ( x)
Find the value of
4x
� e .
�1
( f g)(5)
, giving your answer as an integer.
[4]
(a)
(b)
Let
Show that
�
f 1 ( x) � 0.25ln x .
Write down the domain of
g( x) ( e 1)
x 3
� � .
1
f � .
[2]
[1]
(c)
Find the value of
3. Let f ( x) �ln x � 3, for x � 0 .
1
( g f � )(16) , giving your answer as an integer.
[4]
(a)
(b)
Let
Show that
�1 x�3
f ( x)
� e .
Write down the range of
g( x)
e � �
( x 1)( x 3)
� .
1
f � .
[2]
[1]
4. Let
(c) Find the value of ( f g )(2) , giving your answer as an integer.
3
f( x) � 2 x .
[4]
(a)
(b)
Let
Show that
1
� .
3
�1
f ( x) log
2
x
Write down the range of
g( x) (1 log )
2
� �
2
x .
1
f � .
[2]
[1]
(c) Express ( g f )( x ) in the form
2
ax �bx � c , where a , b and c are integers.
[4]
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