1. Composition of Functions

2. Composition of functions
f ◦ g read “f circle g”
(f ◦ g)(x) = f(g(x))

3. Example If f(x) = x2 and g(x) = x – 3, find a) f ◦ g b) g ◦ f
Note: f ◦ g and g ◦ f are NOT the same
f ◦ g ≠ g ◦ f

4. Example
If f(x) = √(2-x) and g(x) = √(x), find f ◦ g and its domain

5. Three or more functions
(f ◦ g ◦ h)(x) = f(g(h(x)))
Find f ◦ g ◦ h if f(x) = x/(x+1) g(x) = x h(x) = x + 3

6. Can imply composed functions from a single function
F(x) = sin√(x)
can express as f ◦ g if f(x) = sinx and g(x) = √(x)
Express F(x) = (x + 1)5 as f ◦ g