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f x ( ) g x ( )
X
Y 10 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10
Composition of Functions
Composition of Functions Warm Up
- a) If f ( x ) and g ( x ) are polynomial functions, use the two tables of values below to complete the table of values for f ( g ( x )). x f ( x ) 0 3 1 4 2 5 3 6 4 7
x g ( x ) -2 4 -1 1 0 0 1 1 2 4
x f (g( x ))
b) Let h ( x ) = f ( g ( x )). Write a possible mathematical model for h ( x ).
- a) Use the graph for the functions f ( x ) and g ( x ) below to graph y = f ( g ( x )).
b) Let h ( x ) = f ( g ( x )). Write a mathematical model for h ( x ).
X
Y
8 6 4 2 -8 -6 -4 -2 2 4 6 8
Composition of Functions Worksheet
- a) If f ( x ) and g ( x ) are linear functions, use the two tables of values below to complete the table of values for f (g( x )).
x f ( x ) -2 - -1 - 0 0 1 3 2 6
x g ( x ) -6 - -3 - 0 0 3 1 6 2
x f (g( x ))
b) Write mathematical models for f ( x ) and g ( x ).
c) Find f ๎
^ and g ๎
.
d) Let h ( x ) = f ( g ( x )). Write a mathematical model for h ( x ).
- a) If f ( x ) and g( x ) are linear functions, use the two tables of values below to complete the table of values for f ( g ( x )).
x f ( x ) -2 - -1 - 0 - 1 - 2 0
x g ( x ) -8 - -6 - -4 0 -2 1 0 2
x f (g( x ))
b) Write mathematical models for f ( x ) and g ( x ).
c) Find f ๎
^ and g ๎
.
d) Let h ( x ) = f ( g ( x )). Write a mathematical model for h ( x ).
- What do you observe about the composition of inverse functions? Why do you think this happens?
- a) If the function g is the inverse of the function f predict f ( g ( x )) and g ( f ( x )).
b) Check your prediction given g ( x ) = 2 x and f ( x ) = 12 x.
7. Given f ( x ) =^3 x + 1 and g ( x ) = x +1^3 show that g ( x ) and f ( x ) are not inverse functions.
- Given f ( x ) = 3 x โ 2 and g ( x ) = 13 x + 23 , determine if g( x ) and f ( x ) inverse functions? Show the
analysis that leads to your conclusion.
