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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = 1/2 log(2x)
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.e1-2x = 4
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = log(-2x)
In problem, solve each equation.(e4)x . ex2 = e12
A function y = f(x) is increasing on the interval (0, 5). What conclusions can you draw about the graph of y = f-1(x)?
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.9x + 4 ∙ 3x - 3 = 0
If 4x = 7, what does 4-2x equal?
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e* + e*
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = 3 + log3(x + 2)
A function y = f(x) is decreasing on the interval (0, 5). What conclusions can you draw about the graph of y= f-1(x)?
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.4x - 14 ∙ 4-x = 5
If 2x = 3, what does 4 equal?
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. et + e* = 3 2
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = 2 - log3(x + 1)
Find the inverse of the linear functionf(x) = mx + b m ≠ 0
If 3-x = 2, what does 32x equal?
Suppose that f(x) = log2(x - 2) + 1.(a) Graph f.(b) What is f(6)? What point is on the graph of f?(c) Solve f(x) = 4. What point is on the graph of f?(d) Based on the graph drawn in part (a), solve f(x) > 0.(e) Find f-1(x). Graph f-1 on the same Cartesian plane as f.
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. e* - e* = 2 2
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = ex+2 – 3
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = 3ex + 2
Find the inverse of the function f(x) = Vr² – x² 0 < xsr
If 5-x = 3, what does 53x equal?
Suppose that f(x) = log3(x + 1) - 4.(a) Graph f.(b) What is f(8)? What point is on the graph of f?(c) Solve f(x) = -3. What point is on the graph of f?(d) Based on the graph drawn in part (a), solve f(x) < 0.(e) Find f-1(x). Graph f-1 on the same Cartesian plane as f.
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. et - e-x -2
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = 2x/3 + 4
A function f has an inverse function. If the graph off lies in quadrant I, in which quadrant does the graph of f-1 lie?
In problem, determine the exponential function whose graph is given. Уд 20 16 12 (2, 9) 8 (0, 1), (-1, }) (1, 3) y = 0 -3 -2 -1 -2F 1 2 3 x
At what height is a Piper Cub whose instruments record an outside temperature of 0°C and a barometric pressure of 300 millimeters of mercury?In problem, use the following result: If x is the atmospheric pressure (measured in millimeters of mercury), then the formula for the altitude h(x)
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log5 x + log3 x = 1
In problem, use the given function f to:(a) Find the domain of f.(b) Graph f.(c) From the graph, determine the range and any asymptotes of f.(d) Find f-1, the inverse of f.(e) Find the domain and the range of f-1.(f) Graph f-1.f(x) = -3x+1
A function f has an inverse function. If the graph off lies in quadrant II, in which quadrant does the graph of f-1 lie?
In problem, determine the exponential function whose graph is given. 20 16 12 8- (1, 5) 4 (-1, ) (0, 1) y = 0 3 -2 -1 -2E 2 3 x
How high is a mountain if instruments placed on its peak record a temperature of 5°C and a barometric pressure of 500 millimeters of mercury?In problem, use the following result: If x is the atmospheric pressure (measured in millimeters of mercury), then the formula for the altitude h(x)
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log2 x + log6 x = 3
The function f(x) = |x| is not one-to-one. Find a suitable restriction on the domain off so that the new function that results is one-to-one. Then find the inverse of f.
In problem, solve each equation.log3 x = 2
In problem, determine the exponential function whose graph is given. yA (-1, -ह) (0, –1) 3४।= 0 - उ?ै 2. (1, -6) -1 -10 -20 -30 (2, –36) -40
An amplifier€™s power output P (in watts) is related to its decibel voltage gain d by the formula P = 25e0.1d(a) Find the power output for a decibel voltage gain of 4 decibels.(b) For a power output of 50 watts, what is the decibel voltage gain?
f(x) = log2(x + 3) and g(x) = log2(3x + 1).(a) Solve f(x) = 3. What point is on the graph of f?(b) Solve g(x) = 4. What point is on the graph of g?(c) Solve f (x) = g(x). Do the graphs off and g intersect? If so, where?(d) Solve (f + g)(x) = 7.(e) Solve (f - g)(x) = 2.
The function f(x) = x4 is not one-to-one. Find a suitable restriction on the domain off so that the new function that results is one-to-one. Then find the inverse of f.
In problem, solve each equation.log5 x = 3
In problem, determine the exponential function whose graph is given. УА (0, –1) 2 з у-0 3х (1, -e) (-1, -) -4- (2, -e?) -8 -12-
A telescope is limited in its usefulness by the brightness of the star that it is aimed at and by the diameter of its lens. One measure of a star's brightness is its magnitude; the dimmer the star, the larger its magnitude. A formula for the limiting magnitude L of a telescope, that is,
f(x) = log3(x + 5) and g(x) = log3(x - 1).(a) Solve f(x) = 2. What point is on the graph of f?(b) Solve g(x) = 3. What point is on the graph of g?(c) Solve f(x) = g(x). Do the graphs of f and g intersect? If so, where?(d) Solve (f + g)(x) = 3.(e) Solve (f - g)(x) = 2.
Taking into account reaction time, the distance d (in feet) that a car requires to come to a complete stop while traveling r miles per hour is given by the functiond(r) = 6.97r - 90.39(a) Express the speed r at which the car is traveling as a function of the distance d required to come to a
In problem, solve each equation.log2(2x + 1) = 3
Find an exponential function with horizontal asymptote y = 2 whose graph contains the points (0, 3) and (1, 5).
The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formulawhere s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.(a) How many years will it take for a piece of machinery to decline in
In problem, solve each equation.log3(3x - 2) = 2
The head circumference C of a child is related to the height H of the child (both in inches) through the functionH(C) = 2.15C - 10.53(a) Express the head circumference C as a function of height H.(b) Verify that C = C(H) is the inverse of 11 = 11(C) by showing that H (C(H)) = Hand C(H(C)) = C.(c)
A child’s grandparents purchase a $10,000 bond fund that matures in 18 years to be used for her college education. The bond fund pays 4% interest compounded semiannually. How much will the bond fund be worth at maturity? What is the effective rate of interest? How long will it take the bond to
Find an exponential function with horizontal asymptote y = -3 whose graph contains the points (0, -2) and (-2, 1).
(a) If f(x) = 5x-1 and g(x) = 2x+1, graph f and g on the same Cartesian plane.(b) Find the point(s) of intersection of the graphs of f and g by solving f(x) = g(x). Label any intersection points on the graph drawn in part (a).(c) Based on the graph, solve f(x) > g(x).
In problem, solve each equation.logx 4 = 2
One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W(h) = 50 + 2.3(h - 60)(a) What is the ideal weight of a 6-foot male?(b) Express the height h as a function of weight W.(c) Verify that h = h(W) is the inverse of W = W(h) by
A child’s grandparents wish to purchase a bond that matures in 18 years to be used for her college education. The bond pays 4% interest compounded semiannually. How much should they pay so that the bond will be worth $85,000 at maturity?
Suppose that f(x) = 2x.(a) What is f(4)? What point is on the graph of f?(b) If f(x) = 1/16 what is x? What point is on the graph of f?
(a) Graph f(x) = 3x and g(x) = 10 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 3x, and g(x) = 10 on the graph drawn in part (a).(c) Solve f (x) = g(x) and label the point of intersection on the graph drawn in part (a).
The functionconverts a temperature from C degrees Celsius to F degrees Fahrenheit.(a) Express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F.(b) Verify that C = C(F) is the inverse of F = F(C) by showing that C(F(C)) = C and F(C(F)) = F.(c) What is the
First Colonial Bankshares Corporation advertised the following IRA investment plans.For each $5000 Maturity Value DesiredDeposit: ……………………………….. At a Term of:$620.17 ……………………………………. 20 Years$1045.02 ……………………………………. 15
Suppose that f(x) = 3x.(a) What is f(4)? What point is on the graph of f?(b) If f(x) = 1/9, what is x? What point is on the graph of f?
(a) Graph f(x) = 2x and g(x) = 12 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2x, and g(x) = 12 on the graph drawn in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).
In problem, solve each equation.ln ex = 5
The function T(g) = 4675 + 0.25(g - 33,950) represents the 2009 federal income tax T (in dollars) due for a "single" filer whose modified adjusted gross income is g dollars, where 33,950 ≤ g ≤ 82,250.(a) What is the domain of the function T?(b) Given that the tax due T is an increasing linear
The bones of a prehistoric man found in the desert of New Mexico contain approximately 5% of the original amount of carbon 14. If the half-life of carbon 14 is 5600 years, approximately how long ago did the man die?
Suppose that g(x) = 4x + 2.(a) What is g(-1)? What point is on the graph of g?(b) If g(x) = 66, what is x? What point is on the graph of g?
(a) Graph f(x) = 2x+1 and g(x) = 2-x+2 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 2-x+1, and g(x) = 2-x+2 on the graph draw in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).
In problem, solve each equation.ln e-2x = 8
The function T(g) = 1670 + 0.15(g - 16,700) represents the 2009 federal income tax T (in dollars) due for a "married filing jointly" filer whose modified adjusted gross income is g dollars, where 16,700 ≤ g ≤ 67,900.(a) What is the domain of the function T?(b) Given that the tax due T is an
A skillet is removed from an oven whose temperature is 450°F and placed in a room whose temperature is 70°F. After 5 minutes, the temperature of the skillet is 400°F. How long will it be until its temperature is 150°F?
(a) Graph f (x) = 3-x+1 and g(x) = 3x-2 on the same Cartesian plane.(b) Shade the region bounded by the y-axis, f(x) = 3-x+2, and g(x) = 3x-2 on the graph draw in part (a).(c) Solve f(x) = g(x) and label the point of intersection on the graph drawn in part (a).
In problem, solve each equation.log4 64 = x
Gravity on Earth If a rock falls from a height of 100 meters on Earth, the height H (in meters) after t seconds is approximatelyH(t) = 100 - 4.9t2(a) In general, quadratic functions are not one-to-one. However, the function H is one-to-one. Why?(b) Find the inverse of H and verify your
Suppose that(a) What is H(-6)? What point is on the graph of H?(b) If H(x) = 12, what is x? What point is on the graph of H?(c) Find the zero of H. (Э- х H(x) = - 4.
The annual growth rate of the world's population in 2005 was k = 1.15% = 0.0115. The population of the world in 2005 was 6,451,058,790. Letting t = 0 represent 2005, use the uninhibited growth model to predict the world's population in the year 2015.
(a) Graph f(x) = 2x - 4.(b) Find the zero of f.(c) Based on the graph, solve f(x) < 0.
In problem, solve each equation.log5 625 = x
The period T (in seconds) of a simple pendulum as a function of its length l (in feet) is given by(a) Express the length l as a function of the period T.(b) How long is a pendulum whose period is 3 seconds? T(1) = 27, 32.2
Suppose that(a) What is F(-5)? What point is on the graph of F?(b) If F(x) = 24, what is x? What point is on the graph of F?(c) Find the zero of F. - 3. F(x)
The half-life of radioactive cobalt is 5.27 years. If 100 grams of radioactive cobalt is present now, how much will be present in 20 years? In 40 years?
(a) Graph g(x) = 3x - 9.(b) Find the zero of g.(c) Based on the graph, solve g(x) > 0.
The resident population of the United States in 2008 was 304 million people and was growing at a rate of 0.9% per year. Assuming that this growth rate continues, the model P(t) = 304(1.009)t-2008represents the population P (in millions of people) in year t.(a) According to this model, when will the
In problem, solve each equation.log3 243 = 2x + 1
Givenfind f1-(x). If c ‰ 0, under what conditions on a, b, c, and d is f = f1-? |f(x) ах + b сх + d
In fiscal year 2005, the federal deficit was $319 billion. At that time, 10-year treasury notes were paying 4.25% interest per annum. If the federal government financed this deficit through 10-year notes, how much would it have to pay back in 2015?
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if x
The population of the world in 2009 was 6.78 billion people and was growing at a rate of 1.14% per year. Assuming that this growth rate continues, the model P(t) = 6.78(1.0114)t-2009 represents the population P (in billions of people) in year t.(a) According to this model, when will the
In problem, solve each equation.log6 36 = 5x + 3
Can a one-to-one function and its inverse be equal? What must be true about the graph of f for this to happen? Give some examples to support your conclusion.
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if x < 0 le* if x 2 0 f(x) =
The logistic growth modelrepresents the proportion of new cars with a global positioning system (GPS). Let t = 0 represent 2006, t = 1 represent 2007, and so on.(a) What proportion of new cars in 2006 had a UPS?(b) Determine the maximum proportion of new cars that have a UPS.(c) Using a graphing
In problem, solve each equation.e3x = 10
Shannon€™s diversity index is a measure of the diversity of a population. The diversity index is given by the formulawhere p1 is the proportion of the population that is species 1, p2 is the proportion of the population that is species 2, and so on.(a) According to the U.S. Census Bureau,
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if x < 0 -ex if x 2 0 f(x) = ret
The following data were collected by placing a temperature probe in a portable heater, removing the probe, and then recording temperature over time.Time (sec.) …………………………… Temperature (°F)0 ….………………………………………… 165.071
The value V of a Honda Civic DX that is t years old can be modeled by V(t) = 16,775(0.905)t.(a) According to the model, when will the car be worth $15,000?(b) According to the model, when will the car be worth $8000?(c) According to the model, when will the car be worth $4000?
In problem, solve each equation.e-2x = 1/3
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if x < 0 -e f(x) = if x 2 0 -et
Give an example of a function whose domain is the set of real numbers and that is neither increasing nor decreasing on its domain, but is one-to-one.
The following data represent the wind speed (mph) and wind chill factor at an air temperature of 15°F.(a) Using a graphing utility, draw a scatter diagram with wind speed as the independent variable.(b) Using a graphing utility, build a logarithmic model from the data.(c) Using a graphing utility,
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