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Paper 1 – Composite and Inverse Functions
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Example
Let f ( x) �3x
� 4 and g x
2
( ) 7x
1 � � .
( a ) Find f
1 ( x) .
�
( b ) ( i ) Write down f ( 2 ) .
[ 3 ]
( ii ) Hence , find ( g f )( 2 ) . [ 3 ]
Solution |
( a ) |
y�3x�
4
|
|
� x� 3y�
4
|
( M1 ) for swapping variables |
|
x�4�
3y
|
|
x �
4 y
�
3
|
( A1 ) for changing subject |
|
�1 x �
4 � f
( x)
�
3
|
A1 |
[ 3 ] |
( b ) |
( i ) |
10 |
A1 |
( ii ) ( g f )( 2 ) � g( 10 )
2
( g f)( 2 ) �7 ( 10 ) � 1 ( A1 ) for substitution
( g f)( 2 ) � 699 A1
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