44CHAPTER 1 Functions and Models30. Use the given graph of f to sketch the graph of y 1/fx).Which features of f are the most important in sketching33D1/f(x)? Explain how they are used.52. Use the table to evaluate e(a) f(g(1))(d) g(g(1))(b(e3.1.1.0.53. Use the given graphsexplain why it is unde(a) f(g(2))(d) (gof)(6)31-32 Find (a) f+ g, (b) f- g, (c) fg, and (d) f/g and state theirdomains.31. f(x) = x' + 2x, y(x) = 3x - 132. f(x) = 3 - x. g(x) = Vx² - 133-38 Find the functions (a) fo y. (b) y o f. (c) fof, and (d) y o gand their domains.33. f(x) = 3x + 5, g(x) = x2 + x34. f(x)-x'- 2. g(x) = 1- 4.x35. f(x) Vx + 1. g(x) = 4x 3%3D54. Use the given gf(g(x)) for x =sketch a rough36. f(x) -sinx, g(x) = x² + 137. f(x)-x+1g(x)%3Dx+ 238. f(x) --T+xg(x)%3Dsin 2x39-42 Find foy h.39. (x) 3x-2. g(x)) sin x. h(x) = x²%3D40. f(x) x-4. g(x)= 2", h(x) = vx2.3.

Since you have asked multiple question, we will solve the first question for you. If youwant any…

Answered: 1/f(x). 30. Use the given graph of f to…

1/f(x). 30. Use the given graph of f to sketch the graph of y Which features of f are the most important in sketching y //(x)? Explain how they are used.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 36E

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Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

44
CHAPTER 1 Functions and Models
30. Use the given graph of f to sketch the graph of y 1/fx).
Which features of f are the most important in sketching
33D1/f(x)? Explain how they are used.
52. Use the table to evaluate e
(a) f(g(1))
(d) g(g(1))
(b
(e
3.
1.
1.
0.
53. Use the given graphs
explain why it is unde
(a) f(g(2))
(d) (gof)(6)
31-32 Find (a) f+ g, (b) f- g, (c) fg, and (d) f/g and state their
domains.
31. f(x) = x' + 2x, y(x) = 3x - 1
32. f(x) = 3 - x. g(x) = Vx² - 1
33-38 Find the functions (a) fo y. (b) y o f. (c) fof, and (d) y o g
and their domains.
33. f(x) = 3x + 5, g(x) = x2 + x
34. f(x)-x'- 2. g(x) = 1- 4.x
35. f(x) Vx + 1. g(x) = 4x 3
%3D
54. Use the given g
f(g(x)) for x =
sketch a rough
36. f(x) -sinx, g(x) = x² + 1
37. f(x)-x+
1
g(x)%3D
x+ 2
38. f(x) -
-T+x
g(x)%3Dsin 2x
39-42 Find foy h.
39. (x) 3x-2. g(x)
) sin x. h(x) = x²
%3D
40. f(x) x-4. g(x)= 2", h(x) = vx
2.
3.

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