Composition of Functions

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Presentation transcript:

Composition of Functions

Definition/Mathematical Notation Composition of Functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function. Mathematical Notation: Given functions f(x) and g(x), find: (f ⃘ g)(x) or f(g(x))

Function Machines

Table of Values X f(x) 2 3 7 4 1 9 12 5 6 X g(x) 9 6 4 -3 7 12 5 3 Find (g ⃘ f)(7) f(7)=4 g(4)= -3 So (g ⃘ f)(7)= -3

Graphs Find g(f(-1)) First find f(-1)=0 Now find g(0)= -2 So g(f(-1))= -2

Function Rules Given g(x)=3x+2 and f(x) = x2 + x Find g(f(x)) This time we will replace all x values in the g function with the f function g(f(x))= 3( x ) + 2 Our x is replaced by x2 + x g(f(x) = 3(x2 + x) + 2 g(f(x) = 3x2 + 3x + 2 New function from composition of 2 functions