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mathematics
precalculus

Precalculus 9th edition Michael Sullivan - Solutions

In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log,(x - 1) - loga(x + 6) = loga(x - 2) - loga(x + 3)
In problem, find the domain of each logarithmic function.H(x) = log2(x2 - 3x + 2)
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. H(x)-1
In problem, find the exact value of each logarithm without using a calculator.log1/3 9
In problem, for the given functions f and g, find:a. f ° gb. g ° fc. f ° fd. g ° g f(x) = -x; g(x) = 2x - 4
In problem, for the given functions f and g, find:a. f ° gb. g ° fc. f ° fd. g ° g f(x) = 2x + 3; g(x) = 3x
In problem, find the domain of the composite function f ° g.f(x) = x2 + 1; g(x) = √ x – 1
The decibel level, D, of sound is given by the equationwhere I is the intensity of the sound and I0 = 10-12 watt per square meter.(a) If the shout of a single person measures 80 decibels, how loud will the sound be if two people shout at the same time? That is, how loud would the sound be if the
(a) If $1000 is invested at 5% compounded monthly, how much is there after 8 months?(b) If you want to have $1000 in 9 months, how much do you need to place in a savings account now that pays 5% compounded quarterly?(c) How long does it take to double your money if you can invest it at 6%
A 50-mg sample of a radioactive substance decays to 34 mg after 30 days. How long will it take for there to be 2 mg remaining?
Writeas the sum and/or difference of logarithms. Express powers as factors. 4x3 loga x? - 3x – 18
In problem, solve each equation.log2(x - 4) + log2(x + 4) = 3
Solve equation.7x+3 = ex
In problem, solve each equation.log(x2 + 3) = log(x + 6)
In problem, solve each equation.8 – 2e-x = 4
The following data represent the percent of all drivers by age that have been stopped by the police for any reason within the past year. The median age represents the midpoint of the upper and lower limit for the age range.(a) Using your graphing utility, draw a scatter diagram of the data treating
In problem, solve each equation.log(x + 9) = 2
Suppose that f(x) = log3(x + 2). Solve:(a) f(x) = 0(b) f(x) > 0(c) f(x) = 3
In problem, solve each equation.5x+2 = 125
Solve the equation: log3(x + 1) + log3(2x - 3) = 10g9 9.
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 - log5(x - 2)
Solve the equation 4x-3 = 82x.
In problem, use a calculator to evaluate each expression. Round your answer to three decimal places.In 133
For the polynomial function f(x) = 4x3 + 9x2 - 30x - 8:(a) Find the real zeros of f.(b) Determine the intercepts of the graph of f.(c) Use a graphing utility to approximate the local maxima and local minima.(d) Draw a complete graph of f. Be sure to label the intercepts and turning points.
Given that f(x) = x2 + 2 and g(x) = 2/x-3, find f(g(x)) and state its domain. What is f(g(5))?
In problem, use a calculator to evaluate each expression. Round your answer to three decimal places.log 20
Graph f(x) = 3(x + 1)3 - 2 using transformations.
In problem, use a calculator to evaluate each expression. Round your answer to three decimal places.e3 + 2
Determine the quadratic function whose graph is given in the figure. YA 50 (0, 24) -2 8 -10F Vertex: (4, -8)
In problem, solve each equation.log5 x = 4
(a) Graph the quadratic function f(x) = -x2 + 2x - 3 by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercept(s), if any.(b) Solve f(x) ≤ 0.
In problem, solve each equation.logb 16 = 2
Graph the line 2x - 4y = 16.
In problem, solve each equation.3x = 243
Solve the equation 3(x - 2) = 4(x + 5).
If the point (3, -5) is on the graph of a one-to-one function f, what point must be on the graph f-1?
Find the inverse of f(x) = 2/3x - 5 and check your answer.State the domain and the range of f and f-1.
Determine which of the following points are on the graph of x2 + y2 = 1.(a) (1/2, 1/2)(b) (1/2, √3/2)
Determine whether the function is one-to-one.(a) y = 4x2 + 3(b) y = √x + 3 - 5
For the function f(x) = 2x2 - 3x + 1, find the following:(a) f(3)(b) f(-x)(c) f(x + h)
GivenGiven f(x) = x + 2/x - 2 and g(x) = 2x + 5, find:(a) f ° g and state its domain(b) (g ° f)(-2)(c) (f ° g)(-2) x + 2 f(x)
Is the following graph the graph of a function? If it is, is the function one-to-one? ул 4 4 х -4
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = x2 + 4 x ≥ 0
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
In problem, use a calculator to evaluate each expression. Round your answer to three decimal places. 2 In 5 + log 50 log 4 – In 2
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.25x – 8 ∙ 5x = -16
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = ex+2Figure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
In problem, find functions f and g so that f ° g = H.H(x) = √x2 + 1
In 2008, the federal debt was about $10 trillion. In 2008, the U.S. population was about 304 million. Assuming that the federal debt is increasing about 7.8% per year and the U.S. population is increasing about 0.9% per year, determine the per capita debt (total debt divided by population) in 2020.
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = x2 + 9 x ≥ 0
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
In problem, use a calculator to evaluate each expression. Round your answer to three decimal places. 3 log 80 – In 5 log 5 + In 20
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.36x – 6 ∙ 6x = -9
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = ex - 1Figure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
In problem, find functions f and g so that f ° g = H.H(x) = √1 - x2
If the inflation rate averages 3%, how much will $1000 purchase in 2 years?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = 4/x
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(3-x)
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.3.4x + 4 ∙ 2x + 8 = 0
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 5 €“ e-xFigure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
In problem, find functions f and g so that f ° g = H.H(x) = |2x + 1|
Find a so that the graph of f(x) = loga x contains the point (2, 2).
If the inflation rate averages 2%, how much will $1000 purchase in 3 years?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = -3/x
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 + 3-x
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.2 ∙ 49x + 11 ∙ 7x + 5 = 0
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 9 - 3e-xFigure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
In problem, find functions f and g so that f ° g = H.H(x) = |2x2 – 3|
If the amount that $1000 will purchase is only $950 after 2 years, what was the average inflation rate?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = 1/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) = 1 - ex
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.4x - 10 ∙ 4-x = 3
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 2 €“ e-x/2Figure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
If f(x) =2x3 - 3x2 + 4x -1 and g(x) = 2, find (f ° g)(x) and (g ° f)(x).
If the amount that $1000 will purchase is only $930 after 2 years, what was the average inflation rate?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000
In problem, the function f is one-to-one. Find its inverse and check your answer. Graph f, f-1, and y = x on the same coordinate axes.f(x) = 4/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) = 3ex-2
In problem, solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.3x – 14 ∙ 3-x = 5
In problem, begin with the graph of y = ex[Figure 27] and use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.f(x) = 7 - 3e-2xFigure 27 Уд y = e* • (2, e²) 6 3 (1, e) (-1, ;) (0, 1) y=0 (-2,) 3 х
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.log5(x + 1) - log4(x - 2) = 1
If the average inflation rate is 2%, how long is it until purchasing power is cut in half?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of
In problem, the function f is one-to-one. Find its inverse and check your answer. f(x) 3 + x
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 ln(x + 3)
If f(x) = 2x2 + 5 and g(x) = 3x + a. find a so that the graph of f ° g crosses they-axis at 23.
In problem, solve each equation.7x = 73
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.log2(x - 1) - log6(x + 2) = 2
If the average inflation rate is 4%, how long is it until purchasing power is cut in half?Inflation problem require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of
In problem, the function f is one-to-one. Find its inverse and check your answer. 4 f(x) 2 - x
If f(x) = 3x2 - 7 and g(x) = 2x + a, find a so that the graph of f ° g crosses the y-axis at 68.
In problem, solve each equation.5x = 5-6
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 + ln(2x)
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.41-2x = 2
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex = -x
A zero-coupon bond can be redeemed in 20 years for $10,000. How much should you be willing to pay for it now if you want a return of:(a) 10% compounded monthly?(b) 10% compounded continuously?Problem involves zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will
In problem, the function f is one-to-one. Find its inverse and check your answer. Зх f(x) х
In problem, the graph of a logarithmic function is given. Match each graph to one of the following functions:(a) y = log3 x(b) y = log3(-x)(c) y = -log3 x(d) y = -log3(-x)(e) y = log3 x €“ 1(f) y = log3(x - 1)(g) y = log3(1 - x)(h) y = 1 - log3 x Ул [x = 0 -5 1 x
In problem, solve each equation.2-x = 16
In problem, use the functions f and g to find:(a) f ° g(b) g ° f(c) The domain of f ° g and of g °f(d) The conditions for which f ° g = g ° ff(x) = ax + b; g(x) = cx + d
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.86+3x = 4
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.e2x = x + 2

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