Name: __________________
Class:
Let f(x) = 3x + 1 and g(x) = 1
a. 6x 4
Date: _____________
2x 5. Compute (g f )(x ) .
b. 6x 7
c. 6x d. 14
6x + 14
e. 6x 14
Problem code:
copc06.03.05.09m
Let f (x) = 4 2x
Compute (f g)(x ) .
2
a. 2x
+2
2
2
and g(x) = x + 1 .
b. 2x +2
2
+ 4x
4x
c. x
2
d. 2x
4x + 2
+ 2x
2
2
e. 2x
2
+ 4x
2
Problem code:
copc06.03.05.10m
Compute (f g)(x ) .
3
f(x) = 2 x , g(x) = x
a. 2
b. 2
2
+2
2x + 2
x
c. 4
2
d. 2
+ 2
2x
+ 2
2x
 e. 2
x
2
+ 2
+ 2
Problem code:
copc06.03.05.11bm
4
Let h(x) = 2x
2
2x + 3, k(x) = x, and m(x) = 3 for all x. Compute the following.
h [k (x )]
k [h (x )]
h [m (x )]
Problem code:
copc06.03.05.12
5
Let F (x ) = x
a. (
Problem code:
copc06.03.05.24m
PAGE 1
2
, )
and G(x ) =
x Determine the domain of (F G)(x ) .
b. (0, )
c. [0, )
d. (
, 0)
e. (
, 0]
Name: __________________
6
Class:
Date: _____________
A spherical weather balloon is being inflated in such a way that the radius is given by
r = g (t) = 1 t + 2
2
Assume that r is in meters and t is in seconds, with t = 0 corresponding to the time that inflation begins. If the volume of a
sphere of radius r is given by
3
V(r) = 4 r
3
3
125 m
find the time at which the volume of the balloon is
6
a. t = 1 sec
b. t = 2 sec
c. t = 3 sec
d. t = 5 sec
e. t = 4 sec
Problem code:
copc06.03.05.26m
7
Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature T of the environment by
the function
N (T) = 2T
2
+ 240T 5100 (40 t 90)
Here, N(T) represents the number of bacteria present when the temperature is T degrees Fahrenheit. Also, suppose that t hr after
the experiment begins, the temperature is given by
T(t) = 10t + 40 (0 t 5)
How many bacteria are present when t = 5 hr?
a. 800
b. 700
c. 1200
d. 300
e. 500
Problem code:
copc06.03.05.28m
8
Express each function as a composition of two functions. Compare the data in the left column corresponding to the right.
f (x ) =
3
3x + 6 , g (x ) = x
f (x ) = 3x + 6, g (x ) =
Problem code:
copc06.03.05.29a
PAGE 2
3
x
3
F (x ) = g (x ) F (x ) = g (x ) f (x ) = 3x + 6
f (x ) =
3
3x + 6
Name: __________________
9
Class:
Let a (x ) =
1 , b (x ) =
x
3
Date: _____________
2
x , c(x ) = 2x + 1, d (x ) = x . Express the following functions as a composition of
two of the given functions.
f (x ) =
Problem code:
copc06.03.05.31am
PAGE 3
3
2x + 1
a. f (x ) = (c a)(x )
c. f (x ) = (a c)(x )
e. f (x ) = (c b)(x )
b. f (x ) = (b c)(x )
d. f (x ) = (a d)(x )
f. f (x ) = (d a)(x )
ANSWER KEY
Homework 3.5 Math 3 Fall 2006, Bauerle
1.
b
2
4.
2.
d
3. e
5.
c
6. a
2
2x 2x+3 ; 2x 2x+3 ;
15
3
f (x ) = 3x + 6, g (x ) =
7.
d
8.
F (x ) = g (x ) f (x ) =
ANSWER KEY Page 1
3
f (x ) =
3
x 9. b
3x + 6 ,
3x + 6 , g (x ) = x
3
F (x ) = g (x ) f (x ) = 3x + 6