The price p, in dollars, of a certain commodity and the quantity x sold obey the demand

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red

Given two functions f and g, the , denoted , is defined by

f1g1x22 = f1x2 # g(x).

The domain of the composite function 1f  g21x2 is the same as the domain of g1x2.

In Problems 7 and 8, evaluate each expression using the values given in the table.

In Problems 7 and 8, evaluate each expression using the values given in the table.

In Problems 9 and 10, evaluate each expression using the graphs of and shown in the figure.

In Problems 9 and 10, evaluate each expression using the graphs of and shown in the figure.

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f21

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f22

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f23

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f24

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f25

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f26

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f27

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f28

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f29

In Problems 1120, for the given functions and , find: (a) (b) (c) (d) 1f  g2142 1g  f2122 1f  f30

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2128, find the domain of the composite function f  g.

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 2944, for the given functions and find: (a) (b) (c) (d) State the domain of each composite function. f  g g  f f  f g  g

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 4552, show that 1f  g21x2 = 1g  f21x2 = x.

In Problems 5358, find functions and so that f g f  g = H.

In Problems 5358, find functions and so that f g f  g = H.

In Problems 5358, find functions and so that f g f  g = H.

In Problems 5358, find functions and so that f g f  g = H.

In Problems 5358, find functions and so that f g f  g = H.

In Problems 5358, find functions and so that f g f  g = H.

If and find and f1x2 = 2x g1x2 = 2, 1f  g21x2 3 - 3x2 + 4x - 1

If f1x2 = 1f  f21x2. x + find

If and find a so that the graph of crosses the y-axis at 23

If and find a so that the graph of crosses the y-axis at 68.

In Problems 63 and 64, use the functions f and g to find: (a) (b) (c) the domain of and of (d) the conditions for which

In Problems 63 and 64, use the functions f and g to find: (a) (b) (c) the domain of and of (d) the conditions for which

The surface area S (in square meters) of a hot-air balloon is given by where r is the radius of the balloon (in meters). If the radius r is increasing with time t (in seconds) according to the formula find the surface area S of the balloon as a function of the time t

The volume V (in cubic meters) of the hot-air balloon described in Problem 65 is given by If the radius r is the same function of t as in Problem 65, find the volume V as a function of the time t.

The number N of cars produced at a certain factory in one day after t hours of operation is given by If the cost N1t2 = 100t - 5t C 2 , 0 t 10. V1r2 = 4 3 pr3 . r1t2 = 2 3 t 3 , t 0, S1r2 = 4pr2 408 CHAPTER 6 Exponential and Logarithmic Functions (in dollars) of producing N cars is find the cost C as a function of the time t of operation of the factory

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 find the area A of the oil slick as a function of the time t

The price p, in dollars, of a certain product and the quantity x sold obey the demand equation Suppose that the cost C, in dollars, of producing x units is Assuming that all items produced are sold, find the cost C as a function of the price p. [Hint: Solve for x in the demand equation and then form the composite.]

The price p, in dollars, of a certain commodity and the quantity x sold obey the demand equation Suppose that the cost C, in dollars, of producing x units is Assuming that all items produced are sold, find the cost C as a function of the price p

The volume V of a right circular cylinder of height h and radius r is If the height is twice the radius, express the volume V as a function of r

The volume V of a right circular cone is If the height is twice the radius, express the volume V as a function o

Traders often buy foreign currency in hope of making money when the currencys value changes. For example, on June 5, 2009, one U.S. dollar could purchase 0.7143 Euros, and one Euro could purchase 137.402 yen. Let represent the number of Euros you can buy with x dollars, and let represent the number of yen you can buy with x Euros. (a) Find a function that relates dollars to Euros. (b) Find a function that relates Euros to yen. (c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (d) What is

The function converts a temperature in degrees Fahrenheit, F, to a temperature in degrees Celsius, C. The function , converts a temperature in degrees Celsius to a temperature in kelvins, K. (a) Find a function that converts a temperature in degrees Fahrenheit to a temperature in kelvins. (b) Determine 80 degrees Fahrenheit in kelvins

The manufacturer of a computer is offering two discounts on last years model computer. The first discount is a $200 rebate and the second discount is 20% off the regular price, p. (a) Write a function f that represents the sale price if only the rebate applies. (b) Write a function g that represents the sale price if only the 20% discount applies. (c) Find and . What does each of these functions represent? Which combination of discounts represents a better deal for the consumer? Why?

If and are odd functions, show that the composite function is also odd.

If is an odd function and is an even function, show that the composite functions and are both even.