1. Composition of Functions

2. 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))

3. Function Machines

4. 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

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

6. 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 ) Our x is replaced by x2 + x
g(f(x) = 3(x2 + x) + 2
g(f(x) = 3x2 + 3x New function from composition
of 2 functions