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mathematics
precalculus

Questions and Answers of Precalculus

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
In problem, solve each equation.e3x = e2-x
The domain of a one-to-one function g is (-∞, 0], and its range is [0, ∞). State the domain and the range of g-1.
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.e1-x = 5
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. |(V2)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
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
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
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
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
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
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
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
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
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 0Â°C and a barometric pressure of 300 millimeters of mercury?In problem, use the following result: If x is the
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
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 5Â°C and a barometric pressure of 500 millimeters of mercury?In problem, use the following result: If x is the
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
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
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
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
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
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
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)
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
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
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)
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
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
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
First Colonial Bankshares Corporation advertised the following IRA investment plans.For each $5000 Maturity Value DesiredDeposit: ……………………………….. At a Term of:$620.17
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
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 ≤
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
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
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
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
(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)
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
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
(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
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) =
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
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
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
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
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.) ……………………………

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