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Algebra 2 Unit 5 Lesson 5

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Composition of Functions

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Algebra 2 Unit 5 Lesson 5

  1. 1. There are several ways in which we can put two functions  together.  For example, we could add, subtract, multiply or  divide them... f(x) + g(x) f(x) ­ g(x) f(x)  g(x) f(x) ÷ g(x) Let  f(x) = 2x + 1 g(x) = x2 Find: 1. f(0) + g(­4) 2. f(­3)  g(2) 1
  2. 2. A composition of functions is another way of "putting" two  functions together...but be careful with notation!! ( f    g )(x)  is the composition of f and g,  it does not mean to multiply f and g (f ( g ( x ) )  can also be used as the same notation. Read as:  "f of g of x" 2
  3. 3. With compositions work right to left {or inside outside} (f   g)(x) and f(g(x)) (1) Find g(x) (2) Use this value to find f (g   f)(x) and g(f(x)) (1) Find f(x) (2) Use this value to find g 3
  4. 4. 4
  5. 5. Examples: f(x) = 2x + 1 and g(x) = x2 1. (f     g)(2) 2.  (g    f )(2) 3.  f (g  (3) ) 4.    g( f ( 3 )) 5. f(g(f(­2))) 6. g(g(g(2)) 5
  6. 6. 7.  (f     g) (­1) = 8. f (g (­ 3)) =  9.  (g     f) (­1) = 10.   f (g ( 2 )) 6

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