Analysis and Approaches for IBDP Maths Ebook 1 | Page 25

Front Page
7
Paper 1 Section A – Find the inverse function
and the composite of two functions
Example
Let f ( x) �3x
� 4 and
g x
2
( ) 7x
1
� � .
3
(a)
Find
f
1 ( x)
.
(b) Find ( g f )(2) .
�
[3]
[3]
Solution
(a) y�3x�
4
� x� 3y� 4
(M1) for swapping variables
x�4�
3y
x � 4
y � (A1) for changing subject
3
�1 x � 4
� f ( x)
� A1 N2
3
[3]
(b) f (2)
�3(2) � 4
(M1) for substitution
� 10
( g f )(2)
� g(10)
2
�7(10) � 1
(A1) for substitution
� 699
A1 N3
[3]
Exercise 7
1. Let f ( x) �8x
� 1 and
g x
2
( ) x 5
� � .
(a)
Find
f
1 ( x)
.
(b) Find ( f g )(5) .
�
[3]
[3]
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