Composition of Functions
 Input: 3 Plus 10 A FUNCTION rule changes an INPUT to an OUTPUT Output: 13 Input: 7 Plus 10 A FUNCTION rule changes an INPUT to an OUTPUT Output: Input: 64 Plus 10 A FUNCTION rule changes an INPUT to an OUTPUT Output: Input: x Plus 10 An input doesn't have to be a number. Unknown inputs are often represented by "x" Output: x+10 Input: x Plus 4 Write the OUTPUT expression (no spaces) Output: Input: x Plus 4 HIT OK Output: x+4  Original Input g's output Composition of functions: 2 functions in a row. Is placed into f Composition output Original Input ? g's output ? Composition of functions: 2 functions in a row. Is placed into f ? Composition output ? The result of g( ) is sent thru f( ) It can be written as: f[g(x)] OR: (f ο g)(x) Either way, the function in the MIDDLE goes 1st  Find (f ο g)(x) f[g(x)] Given that: g(x) = 2x "double the input" f(x) = x+1 "input plus one" g ? 2x f ? x+1 Given that: g(x) = 2x "double the input" f(x) = x+1 "input plus one" Find (f ο g)(x) f[g(x)] g x 2x f x+1 2x ? 2x+1 ? Given that: g(x) = 2x "double the input" f(x) = x+1 "input plus one" Numeric Inputs are even easier: Find (f ο g)(6) f[g(6)] g 6 2x f x+1 12 ? 13 ? Given that: g(x) = 2x "double the input" f(x) = x+1 "input plus one" Numeric Inputs are even easier: Find (f ο g)(7) f[g(7)] g 7 2x f x+1 Fill in the OUTPUTS Given that: g(x) = 2x "double the input" f(x) = x+1 "input plus one" Numeric Inputs are even easier: Find (f ο g)(-3) f[g(-3)] g 2x f x+1 Fill in the BLANKS If f(x) = x -5 and if g(x) = x2 Which function is performed 1st? Find (g ο f)(8) f, input minus 5 g, input squared If f(x) = x -5 and if g(x) = x2 Find (g ο f)(8) f x-5 g Fill in the BLANKS x2  Find (f ο g)(-7) If f(x) = x -5 if g(x) = x2 Which function is performed 1st? f, input minus 5 g, input squared functions Find (f ο g)(-7) If f(x) = x -5 if g(x) = x2 function g is in the middle, it goes first g -7 ? x2 ? f ? x-5 ? Phil Lynn DaBlanx Find (f ο g)(-7) If f(x) = x -5 if g(x) = x2 g -7 x2 f x-5  Check ALL composite functions that appy function f 1st The function in the MIDDLE goes first (f ο g) (-6) (g ο f) (-6) f[g(-6)] g[f(-6)] Check ALL composite functions that appy function g 1st The function in the MIDDLE goes first (f ο g) (-6) (g ο f) (-6) g f[g(-6)] g[f(-6)] f   Dirty Clothes ? Laundry Composite Function Machine Clean, wet Clothes ? Dry, clean Clothes ?  (ball) The End ⊜ |
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