Chapter 8 Section 1 MA1032 Data, Functions & Graphs Sidney Butler Michigan Technological University November 28, 2006 S Butler (Michigan Tech) Chapter 8 Section 1 November 28, 2006 1 / 5
Composition The function f ( g ( t )) is said to be a composition of f with g . The function f ( g ( t )) is defined by using the output of the function g as the input to f . Example 1+ t and g ( t ) = √ t . 2 Let f ( t ) = What happens to Domains and Ranges? S Butler (Michigan Tech) Chapter 8 Section 1 November 28, 2006 2 / 5
Decomposition of Functions Go Backwards! Example Let h ( x ) = f ( g ( x )) = e x 2 +1 . Find possible formulas for f ( x ) and g ( x ). S Butler (Michigan Tech) Chapter 8 Section 1 November 28, 2006 3 / 5
Summary Composition Domain & Range Decomposition S Butler (Michigan Tech) Chapter 8 Section 1 November 28, 2006 4 / 5
Exercise Let f 1 ( x ) = x , f 2 ( x ) = 1 1 − x , f 5 ( x ) = x − 1 1 x , f 3 ( x ) = 1 − x , f 4 ( x ) = x , and f 6 ( x ) = x − 1 . Note that x 1 1 − (1 − x ) = 1 1 f 4 ( f 3 ( x )) = 1 − f 3 ( x ) = x = f 2 ( x ) . That is f 4 ( f 3 ( x )) = f 2 ( x ). In fact, if we compose any two of these six functions, we will get one of the six functions. Complete the composition table below. f 1 f 2 f 3 f 4 f 5 f 6 ◦ f 1 f 2 f 3 f 4 f 2 f 5 f 6 S Butler (Michigan Tech) Chapter 8 Section 1 November 28, 2006 5 / 5
Recommend
More recommend
