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40.
MULTI-STEP
Carlos is looking to trade in his old car for a new one. He has 6 payments
remaining on his old car. The dealer is offering 0% financing and a $4000 trade-in with
the purchase of a new car. Carlos plans to take out a 5-year loan on the new car.
a.
If his current monthly payment is $280 and he doesn’t want to pay more than $300
per month on a car, what is the most expensive new car that he can afford?
b.
Describe your solution process.
GEOMETRY
The formula for the area of a circle is
A
= π
r
2
.
a.
Find the inverse of the function.
b.
Use the inverse to find the radius of a circle with an area of 36 square centimeters.
Use the horizontal line test to determine whether the inverse of each function is also
a function.
42.
f
(
x
)
=
2
x
2
43.
f
(
x
)
=
x
3
-
8
44.
g
(
x
)
=
x
4
-
6
x
2
+
1
45.
h
(
x
)
= -
2
x
4
-
x
-
2
46.
g
(
x
)
=
x
5
+
x
2
-
4
x
47.
h
(
x
)
=
x
3
+
x
2
-
6
x
+
12
48.
SHOPPING
Felipe bought a used car. The sales tax rate was 7.25% of the selling price,
and he paid $350 in processing and registration fees. Find the selling price if Felipe
paid a total of $8395.75.
49.
TEMPERATURE
A formula for converting degrees Celsius to Fahrenheit is
F
(
x
)
=
9
_
5
x
+
32.
a.
Find the inverse
F
-
1
(
x
). Show that
F
(
x
) and
F
-
1
(
x
) are inverses.
b.
Explain what purpose
F
-
1
(
x
) serves.
50.
MEASUREMENT
There are approximately 1.852 kilometers in a nautical mile.
a.
Write a function that converts nautical miles to kilometers.
b.
Find the inverse of the function that converts kilometers back to nautical miles.
c.
Using composition of functions, verify that these two functions are inverses.
51.
MULTIPLE REPRESENTATIONS
Consider the functions
y
=
x
n
for
n
=
0, 1, 2,
…
.
a. Graphing
Use a graphing calculator to graph
y
=
x
n
for
n
=
0, 1, 2, 3, and 4.
b. Tabular
For which values of
n
is the inverse a function? Record your results
in a table.
c. Analytical
Make a conjecture about the values of
n
for which the inverse of
f
(
x
)
=
x
n
is a function. Assume that
n
is a whole number.
H.O.T. Problems
Use
H
igher-
O
rder
T
hinking Skills
52.
REASONING
If a relation is
not
a function, then its inverse is
sometimes
,
always
, or
never
a function. Explain your reasoning.
53.
OPEN-ENDED
Give an example of a function and its inverse. Verify that the two
functions are inverses.
54.
CHALLENGE
Give an example of a function that is its own inverse.
55.
CONSTRUCT ARGUMENTS
Show that the inverse of a linear function
y
=
mx
+
b
,
where
m
≠
0 and
x
≠
b,
is also a linear function.
56.
WRITING INMATH
Suppose you have a composition of two functions that are inverses.
When you put in a value of 5 for
x
, why is the result always 5?
41
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|
Lesson 5-3
|
Inverse Functions and Relations