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Ca8e Ppt 6 1

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Ca8e Ppt 6 1

  1. 1. Section 6.1 Composite Functions
  2. 2. 1. Form a Composition Function
  3. 3. Composite Function The composite function, denoted by f  g (read as “ composed with ) or g  f (read as “ composed with ), is defined by ( f  g )( x)  f ( g ( x)) or ( g  f )( x)  g ( f ( x))
  4. 4. Evaluating a Composite Function Example 1: Evaluate the expression using the values in the table. X -1 0 1 2 3 2 -1 -2 -1 2 3 2 3 6 11 a. ( f  g )(-1)  f (g (-1))  f (3)  2
  5. 5. 1. Find the Composition Function
  6. 6. For the given functions and , find: (a) ( f  g )(-1) (b) ( g  f )(0) (c) ( g  g )(1) (d ) ( f  f )(2) 1 f ( x)  2 x  1 g ( x)  x  3 2 1  (a) ( f  g )(-1)  f ( g (-1))  f  (-1)  3  2   7  7  f -   2 -   1  -8  2  2 (b) ( g  f )(0)  g ( f (0))  g  2(0)  1  g - 1  - 1  3  - 1 7 2 2
  7. 7. 1  (c) ( g  g )(1)  g ( g (1))  g  (1)  3  2   5 1 5 5 17  g -    -   3  -  3  -  2 2 2 4 4 (d ) ( f  f )(2)  f ( f (2))  f  2(2)  1  f  4  1  f 4  1  f 3  23  1  6  1  6  1  5

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