Main Ideas/Questions
COMPOSITION
of FUNCTIONS
THE DOMAIN OF
(fog)(x)
EXAMPLE I:
f(x)=x+7; g(x)=x²-4
EXAMPLE 2:
f(x)=3-x: g(x)=
EXAMPLE 3:
f(x)=9-2x': g(x) = 4x+1
Notes/Examples
Another method to combine functions is called a composition.
Given f(x) and g(x), the composite function (fog)(x) is defined as:
The domain of the composite function(/g)(x) is
the domain of g such that g(x) is in the domain off.
Domain of g Domain off
g(x)
a) (fog)(x)
g
For examples 1-5:
Given f(x) and g(x), find each function and state its domain.
a) (fog)(x)
b) (gof)(x)
a) (fog)(x)
f(g(x))
b) (gof)(x)
b) (gof)(x)
Gina Wilson (A things Algebro UC), 2017