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Paper 1 – Restricted Domains for Inverse Functions
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Example
The function f is defined as { x : x � k} such that
1
f � exists .
f x
2
( ) ( x 5 ) 3 � � � . The domain of f is restricted as
( a ) State the range of f .
( b ) Write down the maximum value of k .
( c ) Find the expression of
1
f � .
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Solution
( a ) { y: y� 3 }
A1
( b ) 5 A1
( c )
y� � �
2
( x 5 ) 3
2
� x� ( y�5 ) � 3 ( M1 ) for swapping variables
2 ( y�5 ) � x� 3 y�5� x� 3 y� x�3� 5 ( M1 ) for valid approach
�
� f 1 ( x) � x �3 � 5 A1
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Exercise 2
1 . The function f is defined as
{ x : x � k} such that
1
f � exists .
f x
2
( ) ( x 7 ) 10 � � � � . The domain of f is restricted as
( a ) State the range of f .
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