Chapter 1
Inverse Relations and Functions
Practice
DATE
PERIOD
5
yes
x
4. f(x) = −
+9
yes
2. f(x) = - √$$$
x+3-1
A19
0
y
x
40
Glencoe Precalculus
9/30/09 2:05:04 PM
Answers
Glencoe Precalculus
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
027-042_PCCRMC01_893802.indd 40
Chapter 1
t(h) = −, where h is given in feet. Find the inverse of the function. If
4
the water takes 8 seconds to hit the ground, from what height did the
plane drop the water? t -1(h) = 16h2
√$
h
the water to travel from the plane to the ground is given by the function
12. FIRE FIGHTING Airplanes are often used to drop water on forest fires in
an effort to stop the spread of the fire. The time in seconds it takes for
11. Use the graph of f(x) to graph f -1(x).
g$f(x)% =
'''''''
x2
2−
- 6 + 12 = x
2
√ (2 )
)
( √''''
2x + 12 )2
2x + 3 - 3
g$f(x)% = − = x
2
2
2
2
x
10. f(x) = −
- 6; x ≥ 0; g(x) = √$$$$
2x + 12
f$g(x)% = − - 6 = x
(
2
yes; f (x) = x + 2; x ≥ 0
-1
8. f(x) = √$$$
x-2
x-3
f$g(x)% = 2 −
+3=x
2
x-3
9. f(x) = 2x + 3; g(x) = −
7x + 1
2-x
yes; f -1(x) = − ; x ≠ 2
x+7
2x - 1
6. f(x) = −
Show algebraically that f and g are inverse functions.
no
4
7. f(x) = −
(x - 3)2
yes; f -1(x) = x3 + 1
3
5. f(x) = √$$$
x-1
Determine whether f has an inverse function. If it does, find the
inverse function and state any restrictions on its domain.
yes
3. f(x) = x5 + 5x3
no
1. f(x) = 3⎪x⎥ + 2
Graph each function using a graphing calculator, and apply the
horizontal line test to determine whether its inverse function exists.
Write yes or no.
1-7
NAME
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(
)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
027-042_PCCRMC01_893802.indd 41
4π
2
9.8x
f -1(x) = −
2
x is the pendulum length in meters. Find
the inverse of the function.
√9.8
forth one time is modeled by the function
x
−
, x ≥ 0, where
f(x) = 2π $$
takes for a pendulum to swing back and
0.15
0.15x + 20 - 20
-1
f $f(x)% = − = x
0.15
3. PENDULUM The time, in seconds, it
x - 20
f$f-1(x)% = 0.15 −
+ 20 = x
c. Verify that f(x) and f-1(x) are inverses.
0.15
x - 20
f -1(x) = −
b. Write an equation for the inverse of
the function.
f(x) = 0.15x + 20
a. Write a function for the amount of
money Claire saves, where x is the
amount of her paycheck.
2. SAVINGS Claire saves 15% of every
paycheck that she earns, plus an
additional $20.
c. If the electrician charges $225, how
many hours did the job last? 3 h
the amount the electrician
charges
b. What does x represent in the inverse
function?
the function. f -1(x) = −
x - 60
55
a. Find an equation for the inverse of
Chapter 1
DATE
41
PERIOD
y
4
8
12
x
x
−
; x = surface area
√''
4π
Lesson 1-7
9/30/09 2:05:16 PM
Glencoe Precalculus
No; if you graph the
function, it fails the horizontal
line test.
⎨
6. WAGES During her free time, Daphne
babysits. She charges $4.50 for each
whole hour or any fraction of an hour.
The cost f of x hours of babysitting is
given by
⎧
4.5 +x, if +x, = x
f(x) =
.
4.5 +x + 1, if +x, < x
⎩
Does the function have an inverse?
Explain.
4.8 in.
c. A basketball has a surface area of 278
square inches. What is the radius of
the ball? Round to the nearest tenth.
of sphere and f-1(x) = radius of
sphere.
f-1(x) =
b. Find the inverse of the function.
Explain what each variable
represents.
a. What is the relevant domain of the
function? (0, ∞)
5. BASKETBALL The surface area of a
sphere is given by f(x) = 4πx2, where
x is the radius of the sphere.
0
4
8
12
4. SALE The graph represents the flat-rate
shipping cost of an object that is on sale
by a certain percent. Use the graph of the
function to graph its inverse function.
Inverse Relations and Functions
Word Problem Practice
1. ELECTRICIAN The amount an electrician
charges can be modeled by the function
f(x) = 60 + 55x, where x is the number of
hours worked.
1-7
NAME
Answers (Lesson 1-7)