Transcript Composition of Functions - Lompoc Unified School District

Composition of
Functions
Composition of functions
f◦g
read “f circle g”
(f ◦ g)(x) = f(g(x))
Example
If
f(x) = x2
a) f ◦ g
b) g ◦ f
and g(x) = x – 3,
find
Note: f ◦ g and g ◦ f are NOT the same
f◦g≠g◦f
Example
If f(x) = √(2-x) and g(x) = √(x), find f ◦ g
and its domain
Three or more functions
(f ◦ g ◦ h)(x) = f(g(h(x)))
Find f ◦ g ◦ h if f(x) = x/(x+1)
h(x) = x + 3
g(x) = x10
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