Chapter 8
Joy Zhou
10282009
Chapter 8
8.1, 8.2, 8.3, 8.4, 8.6, 8.8
8.1
(a)
h
(
f
(
t
)) =

t

1

=
braceleftBigg
t

1
if t
≥
1
1

t
if t
<
1
(1)
(c)
h
(
h
(
t
)

1) =

t
 
1

=
braceleftBigg

t

1

t
≥
0
 
t

1

t
<
0
=
t

1
t
≥
1
1

t
0
≤
t
<
1

t

1
t
≤ 
1
t
+ 1

1
< t <
0
(2)
8.3
Note: notice the difference between part (a) and part (b). If you see these types
of problems in the second mid term, please pay attention not to misunderstand
the problem.
(a)
f
(
f
(
x
)) =
a
(
ax
+
b
) +
b
(3)
=
a
2
x
+ (
ab
+
b
)
(4)
(b)
Different from part (a), where
f
(
x
) is given, here
g
(
g
(
x
)) is given and you
are asked to find
g
(
x
). An untold trick is to guess that
g
(
x
) is a linear function.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Suppose
g
(
x
) =
ax
+
b
.
Our goal is to figure out the coefficients
a
and
b
.
Then
g
(
g
(
x
)) can also be written in terms of
a,b
and
x
as
g
(
g
(
x
)) =
a
2
x
+ (
ab
+
b
)
.
Now
g
(
g
(
x
)) is known as 6
x

8, so
a
2
x
+ (
ab
+
b
) = 6
x

8.
To figure out
a
and
b
, match the coefficients of the
x
term and the constant
term:
braceleftBigg
a
2
= 6
ab
+
b
=

8
(5)
8.4
(a)
f
(
x
) = 1
/
2
x
+ 3.
f
(
f
(
x
)) = 1
/
4
x
+ 9
/
2.
f
(
f
(
f
(
x
))) = 1
/
8
x
+ 21
/
4. They
are all linear equations, so their graphs are all straight lines.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 KellyShonttell
 Quadratic equation, Elementary algebra, one degree, Joy Zhou

Click to edit the document details