Explain what it means for a function to be (1) and give an example of such afunction.

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Answered: Explain what it means for a function to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars. (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars R(tdollars gallon (RP(t dollars gallon 2010 dollars P(t) dollars (at pump) R(t) dollars. P(tdollars (at pump) 2010 dollars (R P)(t) 2010 dollars gallon gallon Rit dollars . Pt dollars (at pump) 2010 dollars (R P(t dollars gallon gallon OR(t) dollars gallon 2010 dollars P(t) 2010 dollars gallon P(t) dollars (at pump) (R OR(t)dollars gallon 2010 dollars P(t) dollars (at pump) = (R + P)(t 2010 dollars gallon (b) What are the output units of the new function? O2010 dollars per gallon Odollars per gallon gallons per dollar 2010 dollars per dollar (at pump) Ogallons per 2010 dollar
Square cuts of the same size are cut from a flat rectangular piece of cardboard. The remaining cardboard is folded into a lidless box. Assume that the cardboard originally measures 15 inches by 10 inches. Let be the length of one side of the square-cut (at this point you should stop and draw a picture). (A) Write a function describing the volume of the resulting box in terms of x. V(x)= cubic inches (B) What is an appropriate domain for the volume function? ≤ x ≤ (C) Now write a function describing the surface area of the box in terms of x. S(x)= square inches
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 .
At a local bank, when you open an account, you provide certain information that is stored in the bank's records. The table below shows the names and mailing zip codes of some of the bank's customers. (a) Suppose F is the rule that takes a customer's name and provides their mailing zip code. According to the information in this table, is F a function? Explain your reasoning. (b) Suppose G is the rule that takes a customer's mailing zip code and provides their name. According to the information in this table, is G a function? Explain your reasoning. (c) If the bank is looking for a way to identify specific customers, why would using their zip code not be a good way to do this? What other input might the bank use instead?
Can this be a one to one function?
The ideal weight w (in pounds) of a man is a function of his height h (in inches). This function is defined by w(h) = 5h - 180. (a) What should the ideal weight be for a man 70 in. tall? lb (b) What should the ideal height be for a man who weighs 190 lb? in
State whether the function is increasing, decreasing, or neither.(a) Surface area of a sphere as a function of its radius(b) Temperature at a point on the equator as a function of time( c) Price of an airline ticket as a function of the price of oil(d) Pressure of the gas in a piston as a function of volume
Does the composition of functions display the commutative property? Give an example of each case to illustrate your answer.
Anthropologists can estimate a person's height from the length of certain bones. The height h (in inches) of an adult human female can be modeled by the function h(1) where / is the length (in inches) of the femur, or thigh bone. (a) Find the domain and range of the function. (Round your answers to 2 decimal places.) Domain: ? ↑ ? ↑ Range: ? ↑ (b) Suppose a female's femur was 16 inches long. About how tall was she? (Round your answers to the nearest inch.) ft in Need Help? ? (c) If an anthropologist estimates a female's height to be 5 feet 3 inches, about how long was her femur? (Round your answer to 2 decimal places.) in Read It ↑ Talk to a Tutor = 1.94/+ 28.4, 16 ≤ / ≤ 25,
How can a function be represented algebraically by formula and visuallyby a graph? Give an example?
Lots of mathematical operations are commutative, meaning that you can change the order without changing the answer. Is function composition commutative? That is, if you have two functions f ( x ) and g ( x ) , is it true that f ( g ( x ) ) = g ( f ( x ) ) ? Explain your reasoning.
JUIVE LITC pr DICII. Assume it costs 30 cents to mail a letter weighing one ounce or less, and then 28 cents for each additional ounce or fraction of an ounce. Write a piecewise-defined function P(x) that represents the cost, in cents, of mailing a letter weighing between O and 3 ounces.

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Explain what it means for a function to be (1) and give an example of such a function.