Analysis and Approaches for IBDP Maths Ebook 1 | Page 107

Front Page
37
Paper 2 Section A – Composite trigonometric functions
Example
Let
2
� x �
f ( x) � x � 1, gx ( ) �5cos�
��2
. Let h( x) � ( g f )( x)
.
3
�2
�
(a) Find an expression for hx ( ).
(b) Find the period of h .
(c) Write down the range of h .
[3]
[2]
[2]
Solution
(a) hx ( )
� g( f ( x))
(M1) for composite function
� f( x)
�
�5cos � ��2
� 2 �
(A1) for substitution
�1 1�
� 5cos�
x � ��
2
�3 2�
A1 N3
[3]
(b) The period of h
1
�2�
�
3
(M1) for valid approach
� 6�
A1 N2
[2]
(c) The range of h is { y: �3 � y� 7} . A2 N2
[2]
10
Exercise 37
� x �
1. Let f ( x) �2x
� 3, gx ( ) �3cos�
��5
. Let h( x) � ( g f )( x)
.
�4
�
(a) Find an expression for hx ( ).
(b) Find the period of h .
(c) Write down the range of h .
[3]
[2]
[2]
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