C Challenge
Let
f
(
x
)
=
x
4
+
2
x
3
−
5
x
2
−
10
x
f open x close equals , x to the fourth , plus , 2 x cubed , minus , 5 x squared , minus 10 x and
g
(
x
)
=
x
3
−
3
x
2
−
5
x
+
15
.
g open x close equals , x cubed , minus , 3 x squared , minus 5 x plus 15 . Perform each function operation and simplify, and then find the domain.
-
f
(
x
)
·
g
(
x
)
f open x close middle dot g open x close
-
f
(
x
)
g
(
x
)
fraction f , open x close , over g , open x close end fraction
-
g
(
x
)
f
(
x
)
fraction g , open x close , over f , open x close end fraction
Find each composition of functions. Simplify your answer.
- Let
f
(
x
)
=
1
x
.
f open x close equals , 1 over x , . Find f( f( f(x))).
- Let
f
(
x
)
=
2
x
−
3
.
f open x close equals 2 x minus 3 . Find
f
(
1
+
h
)
−
f
(
1
)
h
,
fraction f . open , 1 plus h , close . minus f , open 1 close , over h end fraction . comma
h
≠
0
.
h not equal to 0 .
- Let
f
(
x
)
=
4
x
−
1
.
f open x close equals 4 x minus 1 . Find
f
(
a
+
h
)
−
f
(
a
)
h
,
fraction f . open , eh plus h , close . minus f , open eh close , over h end fraction . comma
h
≠
0
.
h not equal to 0 .
- Let
f
(
x
)
=
4
x
2
−
1
.
f open x close equals , 4 x squared , minus 1 . Find
f
(
a
+
h
)
−
f
(
a
)
h
,
fraction f . open , eh plus h , close . minus f , open eh close , over h end fraction . comma
h
≠
0
.
h not equal to 0 .
Standardized Test Prep
SAT/ACT
- Let f(x) = x + 5 and
g
(
x
)
=
x
2
−
25
.
g open x close equals , x squared , minus 25 . What is the domain of
f
g
(
x
)
?
f over g . open x close , question mark
- All real numbers
- All real numbers except 5
- All real numbers except
−
5
negative 5
- All real numbers except
−
5
negative 5 and 5
- Let
g
(
x
)
=
x
−
3
g open x close equals x minus 3 and
h
(
x
)
=
x
2
+
6
.
h open x close equals , x squared , plus 6 . What is
(
h
∘
g
)
(
1
)
?
open h composition g close open 1 close question mark
-
−
14
negative 14
- 4
- 10
- 15
- Which number is a solution of
|
3
−
2
x
|
<
5
?
vertical line 3 minus 2 x vertical line less than 5 question mark
-
−
6
negative 6
-
−
1
negative 1
- 2
- 4
Short Response
- What is the coefficient of the
x
3
y
4
x cubed , y to the fourth term in the expansion of
(
3
x
−
y
)
7
?
open 3 x minus y close to the seventh . question mark Show your work.
Mixed Review
See Lesson 6-5.
Solve. Check for extraneous solutions.
-
x
2
+
3
=
x
+
1
square root of x squared , plus 3 end root . equals x plus 1
-
x
+
8
=
(
x
2
+
16
)
1
2
x plus 8 equals . open . x squared , plus 16 . close super 1 half end super
-
x
2
+
9
=
x
+
1
square root of x squared , plus 9 end root . equals x plus 1
-
(
x
2
−
9
)
1
2
−
x
=
−
3
open . x squared , minus 9 . close super 1 half end super . minus x equals negative 3
-
x
2
+
12
−
2
=
x
square root of x squared , plus 12 end root . minus 2 equals x
-
(
3
x
)
1
2
=
(
x
+
6
)
1
2
open , 3 x , close super 1 half end super . equals . open , x plus 6 , close super 1 half end super
See Lesson 5-7.
Expand each binomial.
-
(
x
+
4
)
8
open x plus 4 close to the eighth
-
(
x
+
y
)
6
open x plus y close to the sixth
-
(
2
x
−
y
)
4
open 2 x minus y close to the fourth
-
(
2
x
−
3
y
)
7
open 2 x minus 3 y close to the seventh
-
(
9
−
2
x
)
5
open 9 minus 2 x close to the fifth
-
(
4
x
−
y
)
5
open 4 x minus y close to the fifth
-
(
x
2
+
x
)
4
open , x squared , plus x close to the fourth
-
(
x
2
+
2
y
3
)
6
open , x squared , plus 2 , y cubed , close to the sixth
Get Ready! To prepare for Lesson 6-7, do Exercises 104-106.
See Lesson 3-1.
Graph and solve each system.
-
{
y
=
x
−
6
y
=
x
+
6
left brace . table with 2 rows and 1 column , row1 column 1 , y equals x minus 6 , row2 column 1 , y equals x plus 6 , end table
-
{
y
=
0.5
x
+
1
y
=
2
x
−
2
left brace . table with 2 rows and 2 columns , row1 column 1 , y equals , column 2 0.5 x plus 1 , row2 column 1 , y equals , column 2 2 x minus 2 , end table
-
{
y
=
x
+
4
5
y
=
5
x
−
4
left brace . table with 2 rows and 1 column , row1 column 1 , y equals . fraction x plus 4 , over 5 end fraction , row2 column 1 , y equals 5 x minus 4 , end table
