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CHAPTER 5
Study Guide and Review
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Key Vocabulary
composition of functions
(p. 322)
cube root function
(p. 345)
extraneous solution
(p. 352)
inverse function
(p. 329)
inverse relation
(p. 329)
inflection point
(p. 345)
radical equation
(p. 352)
radical function
(p. 338)
radical inequality
(p. 354)
square root function
(p. 338)
Vocabulary Check
Choose a word or term that best completes each statement.
1.
If both compositions result in the
, then the
functions are inverse functions.
2.
In a(n)
, the results of one function are used
to evaluate a second function.
3.
Equations with radicals that have variables in the radicands
are called
.
4.
Two relations are
if and only if one relation
contains the element (
b, a
) when the other relation contains
the element (
a, b
).
5.
When solving a radical equation, sometimes you will obtain
a number that does not satisfy the original equation. Such
a number is called a(n)
.
6.
The square root function is a type of
.
Concept Check
7.
Explain how to algebraically determine the inverse of a
function.
8.
Explain how to determine the domain of a square root
function.
Key Concepts
Operations on Functions
(Lessons 5-1 and 5-2)
Operation
Definition
Sum
(
f
+
g
)(
x
)
=
f
(
x
)
+
g
(
x
)
Difference (
f
-
g
)(
x
)
=
f
(
x
)
-
g
(
x
)
Product
(
f
⋅
g
)(
x
)
=
f
(
x
)
⋅
g
(
x
)
Quotient
(
f
_
g
)
(
x
)
=
f
(
x
)
_
g
(
x
)
,
g
(
x
)
≠
0
Composition [
f
◦
g
](
x
)
=
f
[
g
(
x
)]
Inverse Functions and Relations
(Lesson 5-3)
• Two functions are inverses if and only if both their
compositions are the identity function.
• The inverse relation is the set of ordered pairs obtained by
exchanging the coordinates of each ordered par.
• The inverse of a function can be found by exchanging the
independent and dependent variables (
x
and
y
, respectively)
and then solving for the dependent variable (
y
).
Square Root and Cube Root Functions
(Lessons 5-4 and 5-5)
• The domain of a square root function is limited to values for
which the function is defined.
• The same techniques used to transform the graph of other
functions can be applied to the graphs of square root and
cube root functions.
Solving Radical Equations
(Lesson 5-6)
• To solve a radical equation:
Step 1
Isolate the radical on one
side of the equation.
Step 2
Raise each side of the equation to
a power equal to the index.
Step 3
Solve the resulting
polynomial equation.
Study Organizer
Use your Foldable to review
the chapter. Working with a
partner can be helpful. Ask
for clarification of concepts
as needed.
Study Guide
for Vocabulary
Review Games and key
vocabulary in 13 languages
C07-037A-888482
Solving Radical Equations
and Inequalities
Rational Exponents
Radical Expressions
SquareRootFunctionsandInequalities
InverseFunctionsandRelations
Operations on Functions
nth Roots
Vocabulary
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