Analysis and Approaches for IBDP Maths Ebook 1 | Page 39

Front Page
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Paper 2 Section A – Solve the composite equation
Example
Let
2
f ( x) � x �3x
� 4 and g( x) �x
� 6 , for x� .
3
(a) Find f (10) .
(b) Find ( g f )( x ).
(c) Solve ( g f )( x) � 0.
[2]
[2]
[3]
Solution
(a) f (10)
2
� (10) �3(10) � 4
(M1) for substitution
� 126
A1 N2
[2]
(b) ( g f )( x )
� g( f ( x))
� f( x) � 6
(M1) for composite function
2
� x � x� �
2
3 4 6
� x �3x� 2
A1 N2
(c) ( g f )( x) � 0
2
x �3x� 2 � 0
( x� 2)( x�1) � 0
(M1) for factorization
x �� 2 or x �� 1
A2 N3
[2]
[3]
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