13.1.10: Chapter 10
( \newcommand{\kernel}{\mathrm{null}\,}\)
Be Prepared
ⓐ f(4)=; ⓑ g(f(4))=
x=−23y+4
x
x
ⓐ 1; ⓑ 1
ⓐ 12; ⓑ 3
x=9,x=−9
19
x=7
ⓐ 1; ⓑ a
(x2y)13
2.565
x=4,x=−4
x=2,x=3
x=−5,x=1
Try It
ⓐ 15x+1 ⓑ 15x−9
ⓒ 15x2−7x−2
ⓐ 24x−23 ⓑ 24x−23
ⓒ 24x2−38x+15
ⓐ –8 ⓑ 5 ⓒ 40
ⓐ 65 ⓑ 10 ⓒ 5
ⓐ One-to-one function
ⓑ Function; not one-to-one
ⓐ Not a function
ⓑ Function; not one-to-one
ⓐ Not a function ⓑ One-to-one function
ⓐ Function; not one-to-one ⓑ One-to-one function
Inverse function: {(4,0),(7,1),(10,2),(13,3)}. Domain: {4,7,10,13}. Range: {0,1,2,3}.
Inverse function: {(4,−1),(1,−2),(0,−3),(2,−4)}. Domain: {0,1,2,4}. Range: {−4,−3,−2,−1}.
g(f(x))=x, and f(g(x))=x, so they are inverses.
g(f(x))=x, and f(g(x))=x, so they are inverses.
f−1(x)=x+35
f−1(x)=x−58
f−1(x)=x5+23
f−1(x)=x4+76
x=2
x=4
x=−1,x=2
x=−2,x=3
ⓐ $22,332.96
ⓑ $22,362.49 ⓒ $22,377.37
ⓐ $21,071.81 ⓑ $21,137.04
ⓒ $21,170.00
She will find 166 bacteria.
They will find 1,102 viruses.
ⓐ log39=2
ⓑ log7√7=12 ⓒ log13127=x
ⓐ log464=3
ⓑ log43√4=13 ⓒ log12132=x
ⓐ 64=43
ⓑ 1=x0 ⓒ 1100=10−2
ⓐ 27=33 ⓑ 1=30
ⓒ 110=10−1
ⓐ x=8 ⓑ x=125 ⓒ x=2
ⓐ
x=9 ⓑ x=243 ⓒ x=3
ⓐ
2 ⓑ 12 ⓒ −5
ⓐ 2 ⓑ 13 ⓒ −2
ⓐ
a=11
ⓑ x=e7
ⓐ
a=4
ⓑ x=e9
ⓐ
x=13
ⓑ x=2
ⓐ
x=6
ⓑ x=1
The quiet dishwashers have a decibel level of 50 dB.
The decibel level of heavy traffic is 90 dB.
The intensity of the 1906 earthquake was about 8 times the intensity of the 1989 earthquake.
The intensity of the earthquake in Chile was about 1,259 times the intensity of the earthquake in Los Angeles.
ⓐ 0 ⓑ 1
ⓐ 0 ⓑ 1
ⓐ 15 ⓑ 4
ⓐ 8 ⓑ 15
ⓐ 1+log3x
ⓑ 3+log2x+log2y
ⓐ 1+log9x
ⓑ 3+log3x+log3y
ⓐ log43−1 ⓑ logx−3
ⓐ log25−2 ⓑ 1−logy
ⓐ 4log75 ⓑ 100·logx
ⓐ 7log23 ⓑ 20·logx
log25+4log2x+2log2y
log37+5log3x+3log3y
15(4log4x−12−3log4y−2log4z)
13(2log3x−log35−log3y−log3z)
log25xy
log36xy
log2x3(x−1)2
logx2(x+1)2
3.402
2.379
x=6
x=4
x=4
x=8
x=3
x=8
x=log43log7≈1.933
x=log98log8≈2.205
x=ln9+2≈4.197
x=ln52≈0.805
r≈9.3%
r≈11.9%
There will be 62,500 bacteria.
There will be 47,700 bacteria.
There will be 6.44 mg left.
There will be 31.5 mg left.
Section 10.1 Exercises
ⓐ 8x+23 ⓑ 8x+11 ⓒ
8x2+26x+15
ⓐ 24x+1 ⓑ 24x−19
ⓒ 24x2−14x−5
ⓐ 6x2−9x ⓑ 18x2−9x
ⓒ 6x3−9x2
ⓐ 2x2+3 ⓑ 4x2−4x+3
ⓒ 2x3−x2+4x−2
ⓐ 245 ⓑ 104 ⓒ 53
ⓐ 250 ⓑ 14 ⓒ 77
Function; not one-to-one
One-to-one function
ⓐ Not a function ⓑ Function; not one-to-one
ⓐ One-to-one function
ⓑ Function; not one-to-one
Inverse function: {(1,2),(2,4),(3,6),(4,8)}. Domain: {1,2,3,4}. Range: {2,4,6,8}.
Inverse function: {(−2,0),(3,1),(7,2),(12,3)}. Domain: {−2,3,7,12}. Range: {0,1,2,3}.
Inverse function: {(−3,−2),(−1,−1),(1,0),(3,1)}. Domain: {−3,−1,1,3}. Range: {−2,−1,0,1}.
g(f(x))=x, and f(g(x))=x, so they are inverses.
g(f(x))=x, and f(g(x))=x, so they are inverses.
g(f(x))=x, and f(g(x))=x, so they are inverses.
g(f(x))=x, and f(g(x))=x, so they are inverses (for nonnegative x).
f−1(x)=x+12
f−1(x)=x9
f−1(x)=6x
f−1(x)=x+76
f−1(x)=x−5−2
f−1(x)=√x−6
f−1(x)=3√x+4
f−1(x)=1x−2
f−1(x)=x2+2, x≥0
f−1(x)=x3+3
f−1(x)=x4+59, x≥0
f−1(x)=x5−5−3
Answers will vary.
Section 10.2 Exercises
x=4
x=−1
x=−1,x=1
x=1
x=−1
x=2
x=−1,x=2
ⓕ
ⓐ
ⓔ
ⓐ $7,387.28 ⓑ $7,434.57 ⓒ $7,459.12
$36,945.28
162 bacteria
288,929,825
Answers will vary.
Answers will vary.
Section 10.3 Exercises
log232=5
log5125=3
log1100=−2
logx3√6=13
log175√17=x
log13181=4
log4164=−3
lnx=3
64=26
32=x5
1=70
9=91
1,000=103
43=ex
x=11
x=4
x=125
x=1243
x=2
x=−2
2
0
13
−2
−3
−2
a=9
a=3
a=23√3
x=e4
x=5
x=17
x=6
x=3
x=−5√5,x=5√5
x=−5,x=5
A whisper has a decibel level of 20 dB.
The sound of a garbage disposal has a decibel level of 100 dB.
The intensity of the 1994 Northridge earthquake in the Los Angeles area was about 40 times the intensity of the 2014 earthquake.
Answers will vary.
Answers will vary.
Section 10.4 Exercises
ⓐ 0 ⓑ 1
ⓐ 10 ⓑ 10
ⓐ 15 ⓑ −4
ⓐ √3 ⓑ −1
ⓐ 3 ⓑ 7
log58+log5y
4+log3x+log3y
3+logy
log65−1
3−log5x
4−logy
4−ln16
5log2x
−3logx
13log5x
3√4lnx
log23+5log2x+3log2y
14log521+3log5y
log54+log5a+3log5b
+4log5c−2log5d
23log3x−3−4log3y
12log3(3x+2y2)−log35−2log3z
13(log53+2log5x−log54
−3log5y−log5z)
2
2
log25x−1
log52xy
log3x6y9
0
lnx3y4z2
log(2x+3)2·√x+1
2.379
1.674
5.542
Answers will vary.
Answers will vary.
Section 10.5 Exercises
x=7
x=4
x=1, x=3
x=8
x=3
x=20
x=3
x=6
x=53
x=log74log2≈6.209
x=log112log4≈3.404
x=ln8≈2.079
x=log8log13≈−1.893
x=ln3−2≈−0.901
x=ln163≈0.924
x=ln6≈1.792
x=ln8+1≈3.079
x=5
x=−4,x=5
a=3
x=e9
x=7
x=3
x=2
x=6
x=5
x=log10log12≈−3.322
x=ln7−5≈−3.054
6.9%
13.9 years
122,070 bacteria
8 times as large as the original population
0.03 ml
Answers will vary.
Review Exercises
ⓐ 4x2+12x ⓑ 16x2+12x ⓒ 4x3+12x2
ⓐ −123 ⓑ 356 ⓒ 41
Function; not one-to-one
ⓐ Function; not one-to-one ⓑ Not a function
Inverse function: {(10,−3),(5,−2),(2,−1),(1,0)}. Domain: {1,2,5,10}. Range: {−3,−2,−1,0}.
g(f(x))=x, and f(g(x))=x, so they are inverses.
f−1(x)=x+116
f−1(x)=1x−5
x=−2,x=2
x=−1
x=−3,x=5
$163,323.40
330,259,000
log11,000=−3
ln16=y
100000=105
x=5
x=4
0
x=e−3
x=8
90 dB
ⓐ 13 ⓑ −9
ⓐ 8 ⓑ 5
4+logm
5−ln2
17log4z
log58+2log5a+6log5b
+log5c−3log5d
13(log67+2log6x−1−3log6y
−5log6z)
log3x3y7
log4√y(y−3)2
5.047
x=4
x=3
x=log101log2≈6.658
x=log7log13≈−1.771
x=ln15+4≈6.708
11.6 years
12.7 months
Practice Test
ⓐ 48x−17 ⓑ 48x+5
ⓒ 48x2−10x−3
ⓐ Not a function ⓑ One-to-one function
f−1(x)=5√x+9
x=5
ⓐ $31,250.74 ⓑ $31,302.29 ⓒ $31,328.32
343=73
0
40 dB
2+log5a+log5b
14(log25+3log2x−4−2log2y
−7log2z)
log6√x(x+5)3
x=6
x=ln8+4≈6.079
1,921 bacteria