Algebra 2 Composite Functions
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What's Inside
Composite Functions

 

 Here's a tricky one ...

 Let's say we have:
 

 

F(X) = 2X2 - 5X + 6

G(X) = 3X - 4

 

What is G(F(X)) ?
 
 The rule is that when we have something inside the parenthesis
 substitute it for the variable.
 
 Start from the outside:
 
  G(X) = 3X - 4
  G(F(X)) = 3(F(X)) - 4
 
 We know that F(X) = 2X 2 - 5X + 6,
 so substitute that in for the F(X) ...
 
  G(F(X)) = 3(F(X)) - 4
  G(F(X)) = 3(2X2 - 5X + 6) - 4
  G(F(X)) = 6X2 - 15X + 18 - 4
  G(F(X)) = 6X2 - 15X + 14
 
 OK, that was G(F(X)), how about F(G(X))?
 
  F(X) = 2X2 - 5X + 6
  G(X) = 3X - 4
 
 So take F(X) and put G(X) in for X ...
 
  F(X) = 2(G(X))2 - 5(G(X)) + 6
 
 and since G(X) = 3X - 4, we can substitute 3X - 4 for G(X),
 and work the problem ...
 
  F(X) = 2(G(x))2 - 5(G(x)) + 6
  F(X) = 2(3X - 4)2 - 5(3X - 4) + 6
  F(X) = 2(9X2 - 24X + 16) - 15X + 20 + 6
  F(X) = 18X2 - 48X + 32 - 15X + 26
  F(X) = 18X2 - 63X + 58
 

   copyright 2005 Bruce Kirkpatrick

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