Analysis and Approaches for IBDP Maths Ebook 2 | Page 20

Your Practice Set – Analysis and Approaches for IBDP Mathematics
3
Paper 1 Section A – Odd and Even Functions
Example
The function f and g are defined as
f ( x)
6
� and
x
g x
3
( ) x 4
� � , x� .
(a) Find the expression of ( g f )( x ).
(b) Show that ( g f )( x ) is an even function.
(c) Write down the range of ( g f )( x ).
[2]
[2]
[2]
Solution
(a) ( g f )( x) �
3
f ( x) � 4
3 6
( g f )( x) x 4
� � M1
(b)
2
( g f )( x) x 4
� � A1
2
( g f )( x) ( x) 4
� � � � M1
[2]
2
( g f )( x) x 4
� � � A1
( g f )( �x) � ( g f )( x)
Thus, ( g f )( x ) is an even function. AG
(c) { y: y� 2}
A2
[2]
[2]
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