Apps. and Interpretation HL Practice Paper Book | Page 15

3

Functions

� The function y � f ( x)

: 1 . f( a ): Functional value when x� a

2 . Domain : Set of values of x 3 . Range : Set of values of y

�	ax � b Properties of rational function y � cx � d
1 .		1 y � : Reciprocal function x
2 .		a y � : Horizontal asymptote c
3 .		d x �� : Vertical asymptote c

� 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

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