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mathematics
precalculus

Questions and Answers of Precalculus

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 €“
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
In problem, the function f is one-to-one. Find its inverse and check your answer. 2x f(x) =
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 €“
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 ° f f(x) 8(х) сх + d' ах + b тх
The surface area S (in square meters) of a hot-air balloon is given byS(r) = 4πr2where r is the radius of the balloon (in meters). If the radius r is increasing with time t (in seconds) according to
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.3x2+x = √3
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex = x2
How much should a $10,000 facevalue, zero-coupon bond, maturing in 10 years, be sold for now if its rate of return is to be 8% compounded annually?Problem involves zero-coupon bonds. A zero-coupon
In problem, the function f is one-to-one. Find its inverse and check your answer. 2x f(x) Зх — 1
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 €“
In problem, solve each equation. 25
The volume V (in cubic meters) of the hot-air balloon described in Problem 65 is given by V(r) = 4/3πr3. If the radius r is the same function of at as in Problem 65, find the volume V as a function
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.4x-x2 = 1/2
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex = x3
The number N of cars produced at a certain factory in one day after t hours of operation is given by N (t) = 100t - 5t2, 0 ≤ t ≤ 10. If the cost C (in dollars) of producing N cars is C(N) =
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.logx 64 = -3
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.In x = -x
In problem, the function f is one-to-one. Find its inverse and check your answer. Зx + 4 f(х) 2х — 3
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 €“
In problem, solve each equation.22x-1 = 4
The spread of oil leaking from a tanker is in the shape of a circle. If the radius r (in feet) of the spread after t hours is r(t) = 200 √t, find the area A of the oil slick as a function of the
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.log√2 x = -6
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.In(2x) = -x + 2
The formulacan be used to find the number of years t required for an investment P to grow to a value A when compounded continuously at an annual rate r.(a) How long will it take to increase an
In problem, the function f is one-to-one. Find its inverse and check your answer. 2х — 3 f(x) 2x
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 €“
In problem, solve each equation.5x+3 = 1/5
In problem, solve each equation.92x ∙ 27x2 = 3-1
In problem, solve each equation.ex2 = e3x ∙ 1/e2
The domain of a one-to-one function g is [0, 15], and its range is (0, 8). 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 three decimal places.log2 xlog2 x = 4
(a) If f(x) = 3x+1 and g(x) = 2x+2, graph f and g on the same Cartesian plane.(b) Find the point(s) of intersection of the graphs off and g by solving f(x) = g(x). Round answers to three decimal
In problem, solve each equation.logx(1/8) = 3
Suppose that g(x) = 5x - 3.(a) What is g(-1)? What point is on the graph of g?(b) If g(x) = 122, what is x? What point is on the graph of g?
What rate of interest compounded annually is required to double an investment in 3 years?
The value V of a Chevy Cobalt that is t years old can be modeled by V(t) = 16,500(0.82)t.(a) According to the model, when will the car be worth $9000?(b) According to the model, when will the car be
The price p, in dollars, of a certain product and the quantity x sold obey the demand equationSuppose that the cost C, in dollars, of producing x units isAssuming that all items produced are sold,
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.5x = 3x+2
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.In x = x3 – 1
In problem, the function f is one-to-one. Find its inverse and check your answer. f(x) 2х + 3 х+ 2
(a) The CPI was 163.0 for 1998 and 215.3 for 2008. Assuming that annual inflation remained constant for this time period, determine the average annual inflation rate.(b) Using the inflation rate from
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 €“
In problem, solve each equation.3x3 = 9x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.5x+2 = 7x-2
The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equationSuppose that the cost C, in dollars, of producing x units isAssuming that all items produced are sold,
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.In x = -x2
In problem, the function f is one-to-one. Find its inverse and check your answer. — Зх — 4 х — 2 Г(х)
If the current CPI is 234.2 and the average annual inflation rate is 2.8%, what will be the CPI in 5 years? Problem requires the following discussion. The Consumer Price Index (CPI) indicates the
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 €“
In problem, solve each equation.4x2 = 2x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.92x = 273x-4
The volume V of a right circular cylinder of height h and radius r is If V = πr2h. the height is twice the radius, express the volume V as a function of r.
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex + In x = 4
In problem, the function f is one-to-one. Find its inverse and check your answer. x2 – 4 2x2 |f(x) : x >0
If the average annual inflation rate is 3.1%, how long will it take for the CPI index to double? (A doubling of the CPI index means purchasing power is cut in half.) Problem requires the following
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.8-x+14 = 16x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.252x = 5x2-12
The volume V of a right circular cone is V = ½ πr2h. If the height is twice the radius, express the volume V as a function of r.
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex - In x = 4
In problem, the function f is one-to-one. Find its inverse and check your answer. x² + 3 3x2 f(x)
The base period for the CPI changed in 1998. Under the previous weight and item structure, the CPI for 1995 was 456.5. If the average annual inflation rate was 5.57%, what year was used as the base
In problem, solve each equation.9-x+15 = 27x
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.log3 √x - 2 = 2
Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on June 5, 2009, one U.S. dollar could purchase 0.7143 Euros, and one Euro could
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.e-x = In x
Use the graph of y = f (x) given in Problem 43 to evaluate the following:(a) f(-1)(b) f(1)(c) f-1 (1)(d) f-1(2)Data form problem 43 y = x (1, 2), (0, 1), 1, 0). -3 3х (-2, –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
In problem, solve each equation.3x2-7 = 272x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.2x+1∙8-x = 4
In problem, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.e-x = -In x
The functionconverts a temperature in degrees Fahrenheit, F, to a temperature in degrees Celsius, C. The function K(C) = C + 273, converts a temperature in degrees Celsius to a temperature in
Use the graph of y = f (x) given in Problem 44 to evaluate the following:(a) f(2)(b) f(1)(c) f-1(0)(d) f-1(-1)Data from problem 44 y = x (2. }) (1, 0) 3 x -3 (0, –1) (-2, –2) -3F
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.5x2+8 = 1252x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.8 = 4x2 ∙ 25x
Discounts The manufacturer of a computer is offering two discounts on last year's model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p.(a) Write
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log2(x + 1) - log4 x = 1
If f(7) = 13 and f is one-to-one, what is f-1(13)?
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.4x ∙ 2x2 = 162
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.2x ∙ 5 = 10x
If f and g are odd functions, show that the composite function f ° g is also odd.
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log2(3x + 2) – log4 x = 3
If g(-5) = 3 and g is one-to-one, what is g-1(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
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.log6(x + 3) + log6(x + 4) = 1
If f is an odd function and g is an even function, show that the composite functions f ° g and g ° f are both even.
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log16 x + log4 x + log2 x = 7
The domain of a one-to-one function f is [5, ∞), and its range is [-2, ∞). State the domain and the range of f-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
In problem, solve each equation.ex = e3x+8
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.log(7x - 12) = 2 log x
In problem, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log9 x + 3 log3 x = 14
The domain of a one-to-one function f is [0, ∞), and its range is [5, ∞). State the domain and the range of f-1.

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