Download Sum, Difference, Product, and Quotient of

Name_____________________
Pre-Calculus
Section 1.4 Lecture (Combinations of Functions)
Sum, Difference, Product, and Quotient of Functions
( f + g )( x) = f ( x) + g ( x)
1. Sum:
( f − g )( x) = f ( x) − g ( x)
2. Difference:
3. Product: ( fg )( x) = f ( x) • g ( x)
f
f ( x)
4. Quotient:  ( x) =
, g ( x) ≠ 0
g ( x)
g
1. f ( x) = x and g ( x) = x − 1 . Find the following and specify the domain.
a.) (f+g)(x)=
domain=______________
b.) (f-g)(x)=
domain=_____________
c.)(fg)(x)=
domain=_____________
d.)
domain=_____________
f.) Evaluate the following using the same f and g.
(f+g)(3)
(fg)(4)
(f-g)(2)
_________________
_________________
___________________
Definition of Composition of Two functions:
The composition of the function f with g is
.
The domain of
is the set of all x in the domain of g such that g(x)
is in the domain of f.
2. Given
and
a.)
find the following:
b.)
_____________________
______________________
Domain=______________
Domain=____________________
3. Find two functions f and g such that
.
a.)
b.)
f(x)= ______________
f(x)=________________
g(x)=_______________
g(x)=________________
4. Use the graphs of f and g to evaluate the functions:
graph of f(x)
graph of g(x)
a.) (f+g)(-2)=________________
b.)
=________________
c.)
c.)
=_______________
=________________
Application Example:
5. The number of bacteria in a refrigerated food is
, where T is the temperature of the food in
degrees Celsius. When the food is removed from refrigeration, the
temperature is
, where t is the time (in hours). Find the
following:
a.The composite N(T(t)). What does this function represent?
b.The number of bacteria in the food when t=2 hours.
c.The time when the bacterial count reaches 2000.