Analysis and Approaches for IBDP Maths Ebook 1 | Page 45

Front Page
13
Paper 1 Section A – Composite
and inverse functions
Example
Let
f ( x) log 2
x � .
2
� x , for 0
(a)
(b)
Let
Show that f
1
�1 2
( x) � 2 x
.
Write down the range of
g( x) log 2
x
x � .
3
� , for 0
1
f � .
[2]
[1]
4
(c)
Find the value of
�1
( f g)(4)
, giving your answer as an integer.
[4]
Solution
(a)
(b)
2
y�
log 2
x
2
x� log 2
y
(M1) for swapping variables
2
2 x � y
A1
2 x � y
1
2
2 x � y
1
�1 2
� f ( x) � 2 x
AG N0
Range of
(c) g (4)
� log 4
2
3
1
f � : { y : y , y 0}
� � A1 N1
� log 64
A1
2
�1
( f g)(4)
�
f
1 ( g(4))
�
[2]
[1]
1 (log 2 64)
2 2
log 8
� (M1) for substitution
2
� 2
(M1) for correct formula
� 8
A1 N1
[4]
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