Analysis and Approaches for IBDP Maths Ebook 2 | Page 76

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 24
1. The function f and g are defined by f ( x) �ax � bcos
x and
a and b are constants. It is given that f is an even function.
g( x)
5
�� x , where x� ,
(a) Find the value of a and the value of b .
f( x)
Let hx ( ) � , x� \{0} .
gx ( )
[3]
(b)
Show that h is an odd function.
[2]
b
2
2. The function f and g are defined by f ( x) �asec
x � and g( x) � sin 4x
, where
x
� � � �
x� � � , � \{0} , a and b are constants. It is given that f is an even function.
� 2 2�
(a) Find the value of a and the value of b .
� � � �
Let h( x) � f ( x) � g( x)
, x� � � , � \{0} .
� 2 2�
[3]
(b)
Show that h is an even function.
[2]
x
1
3. The function f and g are defined by f( x) � sin and gx ( ) � 2
2
1 � x
, x� .
(a)
Show that f is an even function.
Let h( x) � g f ( x)
, x� . It is given that h( p)
(b) Express h( � p)
in terms of q .
� q , where p and q are constants.
[2]
[2]
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