Analysis and Approaches for IBDP Maths Ebook 1 | Page 199

Front Page
68
Paper 1 Section B – Properties of functions
Example
ax
Let f( x)
� , �12 � 12
2
x � 4
x � , a� . The graph of f is shown below.
16
The region between x � 2 and x � 8 is shaded.
(a) Show that f ( �x) � � f ( x)
.
(b)
(c)
(d)
2
2 ax( x �12)
Given that f��( x)
�
2 3
( x � 4)
, find the coordinates of all points of inflexion.
[7]
Find the area of the shaded region, giving your answer in terms of a and in the
form pln
q.
[6]
�2
Hence, write down the value of � f ( )dx
in terms of a .
�8
[2]
[2]
Solution
(a) f( � x)
a( �x)
�
2
( � x) � 4
M1A1
�ax
�
2
x � 4
�� f( x)
AG N0
[2]
www.seprodstore.com
191