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mathematics
calculus early transcendentals

Questions and Answers of Calculus Early Transcendentals

Find all the inverses associated with the following functions and state their domains.f(x) = (x - 4)2
Find all the inverses associated with the following functions and state their domains.f(x) = (x + 1)3
Use any means to approximate the intersection point(s) of the graphs of f(x) = ex and g(x) = x123.
Without using a graphing utility, sketch the graph of y = log2 x. Then on the same set of axes, sketch the graphs of y = log2(x - 1), y = log2 x2, y = (log2 x)2, and y = log2 x + 1.
Without using a graphing utility, sketch the graph of y = 2x. Then on the same set of axes, sketch the graphs of y = 2-x, y = 2x - 1, y = 2x + 1, and y = 22x.
The following figure shows the graphs of y = log2 x, y = log4 x, and y = log10 x. Match each curve with the correct function. yA х -1
The following figure shows the graphs of y = 2x, y = 3x, y = 2-x, and y = 3-x. Match each curve with the correct function. Уд х
Determine whether the following statements are true and give an explanation or counterexample.a. If y = 3x, then x = 3√y.b. logb x/logb y = logb x - logb yc. log5 46 = 4 log5 6d. 2 = 10log10 2e. 2
Convert the following expressions to the indicated base.a1/log10 a using base 10, for a > 0 and a ≠ 1
Convert the following expressions to the indicated base.a1/ln a using base e, for a > 0 and a ≠ 1
Convert the following expressions to the indicated base.log2 (x2 + 1) using base e
Convert the following expressions to the indicated base.ln |x| using base 5
Convert the following expressions to the indicated base.3sin x using base e
Convert the following expressions to the indicated base.2x using base e
Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.log6 60
Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.log4 40
Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.log3 30
Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.log2 15
The population P of a small town grows according to the function P(t) = 100 et/50, where t measures the number of years after 2010. How long does it take the population to double?
One hundred grams of a particular radioactive substance decays according to the function m(t) = 100 e-t/650, where t > 0 measures time in years. When does the mass reach 50 grams?
Solve the following equations.53x = 29
Solve the following equations.33x - 4 = 15
Solve the following equations.2x = 55
Solve the following equations.7x = 21
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb b2x5/2/√y
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb √x/3√z
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb √xy/z
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb xz
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb x2
Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the following expressions.logb x/y
Solve the following equations.ln y = 3
Solve the following equations.ln x = -1
Solve the following equations.logb 125 = 3
Solve the following equations.log8 x = 1/3
Solve the following equations.log5 x = -1
Solve the following equations.log10 x = 3
Sketch the graph of the inverse function. y = x y = f(x) х 1
Sketch the graph of the inverse function. y A у3х y = f(x) х
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = -x2 - 4x -
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = x2 - 2x +
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = 6/(x2 - 9),
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = x4 + 4, for
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = √3 - x,
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = √x, for x
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = 4x - 12
Find the inverse function (on the given interval, if specified) and graph both f and f-1 on the same set of axes. Check your work by looking for the required symmetry in the graphs.f(x) = 8 - 4x
The equation y4 = 4x2 is associated with four one-to-one functions f1(x), f2(x), f3(x), and f4(x) (see figure).a. Find the domain and a formula for each function.b. Find the inverse of each function
The unit circle x2 + y2 = 1 consists of four one-to-one functions, f1(x), f2(x), f3(x), and f4(x) (see figure).a. Find the domain and a formula for each function.b. Find the inverse of each function
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 2/(x2 + 1), for x ≥
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = √x + 2, for x ≥ -2
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = x2 + 4, for x ≥ 0
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 3x + 5
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 3x3
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 6 - 4x
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 1/4 x + 1
a. Find the inverse of each function (on the given interval, if specified) and write it in the form y = f-1(x).b. Verify the relationships f(f-1(x)) = x and f-1(f(x)) = x.f(x) = 2x
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = x2 - 2x + 8
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = 1/x2
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = -(6 - x)2
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = 1/(x - 5)
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = |2x + 1|
Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.f(x) = 3x + 4
Sketch a graph of a function that is one-to-one on the intervals (- ∞, -2], and [-2, ∞) but is not one-to-one on (- ∞, ∞).
Sketch a graph of a function that is one-to-one on the interval (- ∞, 0] but is not one-to-one on (- ∞, ∞).
Find four intervals on which f is one-to-one, making each interval as large as possible. y y = f(x) + х -4 -2 2.
Find three intervals on which f is one-to-one, making each interval as large as possible. y. У%3Dfx) + х -3 -2 -1
Express 25 using base e.
For b > 0 with b ≠ 1, what are the domain and range of f(x) = logbx and why?
How is the property bx + y = bxby related to the property logb (xy) = logb x + logb y?
Explain the meaning of logb x.
Express the inverse of f(x) = 3x - 4 in the form y = f-1(x).
Sketch a function that is one-to-one and positive for x ≥ 0. Make a rough sketch of its inverse.
Explain with pictures why (a, b) is on the graph of f whenever (b, a) is on the graph of f-1.
Explain why a function that is not one-to-one on an interval I cannot have an inverse function on I.
Give an example of a function that is one-to-one on the entire real number line.
For b > 0, what are the domain and range of f(x) = bx?

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