Section 2-7
1
Math 150 Lecture Notes
Composition of Functions
Let f and g be functions with domains A and B. Then the functions f + g, f – g, fg, and f/g are
defined as follows:
(f + g)(x) = f(x) + g(x) Domain A ∩ B
(f – g)(x) = f(x) – g(x) Domain A ∩ B
(fg)(x) = f(x)g(x) Domain A ∩ B
)(
)(
)( xg
xf
x
g
f=
Domain {x ∈ A ∩ B | g(x) ≠0}
Given two function f and g, the composite function
gf o
(also called the composition of
f
and
g
) is defined by
))(())(( xgfxgf
=
o.
The domain of gf o is the set of all x in the domain of g such that g(x) is in the domain of f.
f
x
g
gf
o
f(g(x))
g(x)
Example 1: Find f + g, f – g, fg, and f/g and their domains.
4)(
2
−=
xxf
2
2
)( +
=
x
xg
