Chapter

Functions

SUMMARY POINTs

� f g( x) � f ( g( x))

: Composite function when gx ( ) is substituted into f( x )

�

� Steps of finding the inverse function y � f ¹ ( x) of f( x ):
1 .	Start from expressing y in terms of x
2 .	Interchange x and y
3 .	Make y the subject in terms of x

�

Properties of y � f ¹ ( x) :

1 .

1 1 f ( f ^�

� ( x)) � f ( f ( x)) � x

�

2 . The graph of y � f ¹ ( x) is the reflection of the graph of y � f ( x) about y� x

� f

¹ ( x)

� exists only when f( x ) is one-to-one in the restricted domain

�	Variations :
1 .		y �kx, k � 0: y is directly proportional to x
2 .		k y� , k � 0: y is inversely proportional to x x

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