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Question: Find the domain of each function. a.


Find the domain of each function.
a. f(x) = 1 - ex2 / 1 - e1-x2
b. f(x) = 1 + x / ecos x


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> The formula C = 5/9(F – 32), where F ≥ -459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

> The graph off is given. a. Why is f one-to-one? b. What are the domain and range of f -1? c. What is the value of f -1(2)? d. Estimate the value of f -1(0). 1 1

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> Assume that f is a one-to-one function. a. If f(6) = 17, what is f -1(17)? b. If f -1(3) = 2, what is f(2)?

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> An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If t represents the time in minutes since the plane has left the terminal building, let x(t) be the horizontal distance traveled and y(t) be the altitude of

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. у.

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> After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours. Suppose you have had three alcoholic drinks and an hour later, at midnight, your blood alcohol concentration (BAC) is 0.6 mg/mL. a. Find an exponentia

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> The half-life of bismuth-210, 210Bi, is 5 days. a. If a sample has a mass of 200 mg, find the amount remaining after 15 days. b. Find the amount remaining after t days. c. Estimate the amount remaining after 3 weeks. d. Use a graph to estimate th

> A bacteria culture starts with 500 bacteria and doubles in size every half hour. a. How many bacteria are there after 3 hours? b. How many bacteria are there after t hours? c. How many bacteria are there after 40 minutes? d. Graph the population func

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> Use a graph to estimate the values of x such that ex > 1,000,000,000.

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> Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. Find all points of intersection of the graphs correct to one decimal place. Which function grows more rapidly when x is large?

> You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool before eating it. Describe how the temperature of the pie changes as time passes. Then sketch a rough graph of the temperature of the pie as a function of tim

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> The Heaviside function defined in Exercise 59 can also be used to define the ramp function y = ctH(t), which represents a gradual increase in voltage or current in a circuit. a. Sketch the graph of the ramp function y = tH(t). b. Sketch the graph of th

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> Express the function in the form f 0 g 0 h. S(t) = sin2(cos t)

> Express the function in the form f 0 g 0 h. H(x) = 8 2 +|x|

> Express the function in the form f 0 g 0 h. R(x) =√ x − 1

> Express the function in the form f 0 g. u(t) =tan t / 1 + tan t

> Express the function in the form f 0 g. v(t) = sec(t2) tan(t2)

> Express the function in the form f 0 g. G(x) = 3 x/ 1+x

> Express the function in the form f 0 g. F(x) = ∛x / 1 + ∛x

> Express the function in the form f 0 g. F(x) = cos2x

> Express the function in the form f 0 g. F(x) = (2x + x2)4

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> The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; t is measured in hours starting at midnight.) a. What was the power consumption at 6 am? At 6 pm? b. When was the power consumption the lowest?

> Find f 0 g 0 h. f(x) =

> Find f 0 g 0 h. f(x) =|x - 4|, g(x) = 2x, h(x) = √x

> Find f 0 g 0 h. f(x) = 3x - 2

1.99

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