Functions Let f(x) = (x – 2) (8 – x) for 2 < x < 8. (a) Find f(6) and f(- 1). (b) What is the domain of definition of f(x)? (c) Find f(1 – 2t) and give the domain of definition. (d) Find f[f(3)], f[f(5)]. (e) Graph f(x). 3.1. (a) f(6) = (6 – 2) (8 – 6) = 4 · 2 = 8 f(- 1) is not defined since f(x) is defined only for 2 < x < 8. (b) The set of all x such that 2 < x < 8. (c) f(1 – 2t) = {(1 – 21) – 2} {8 – (1 – 21)} = – (1 + 21) (7 + 21) where t is such that 2 < 1– 2t - 7/2
Functions Let f(x) = (x – 2) (8 – x) for 2 < x < 8. (a) Find f(6) and f(- 1). (b) What is the domain of definition of f(x)? (c) Find f(1 – 2t) and give the domain of definition. (d) Find f[f(3)], f[f(5)]. (e) Graph f(x). 3.1. (a) f(6) = (6 – 2) (8 – 6) = 4 · 2 = 8 f(- 1) is not defined since f(x) is defined only for 2 < x < 8. (b) The set of all x such that 2 < x < 8. (c) f(1 – 2t) = {(1 – 21) – 2} {8 – (1 – 21)} = – (1 + 21) (7 + 21) where t is such that 2 < 1– 2t - 7/2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3.1) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
![Functions
Let f(x) = (x – 2) (8 – x) for 2 < x < 8. (a) Find f(6) and f(- 1). (b) What is the domain of definition of
f(x)? (c) Find f(1 – 21) and give the domain of definition. (d) Find f[f(3)], f[f(5)]. (e) Graph f(x).
3.1.
(a) f(6) = (6– 2) (8 – 6) = 4 · 2 = 8
f(- 1) is not defined since f(x) is defined only for 2
8.
(b) The set of all x such that 2 < x < 8.
(c) f(1 – 2t) = {(1 – 2t) – 2} {8 – (1 – 21)} = – (1 + 2t) (7 + 2t) where t is such that 2
- 7/2 <I<- 1/2.
1– 2t
'§ 8; i.e.,
f(x)
(d) f(3) = (3 – 2) (8 – 3) = 5, ƒ [ f(3)] = f(5) = (5 – 2)(8 – 5) = 9.
f(5) = 9 so that f [ f(5)] = f(9) is not defined.
(e) The following table shows f(x) for various values of x.
6
3
4
5
6.
7
8
2.5
7.5
f(x) 0
8.
9
8
5
2.75 2.75
2-
Plot points (2, 0), (3, 5), (4, 8), (5, 9), (6, 8), (7, 5), (8, 0),
(2.5, 2.75), (7.5, 2.75). These points are only a few of the infi-
nitely many points on the required graph shown in the adjoining
Figure 3.5. This set of points defines a curve which is part of a
parabola.
Figure 3.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad530511-9758-42d9-9994-894bc4eea3f3%2F085088be-6395-4557-9de9-066fff39af7d%2Frzn8nqg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Functions
Let f(x) = (x – 2) (8 – x) for 2 < x < 8. (a) Find f(6) and f(- 1). (b) What is the domain of definition of
f(x)? (c) Find f(1 – 21) and give the domain of definition. (d) Find f[f(3)], f[f(5)]. (e) Graph f(x).
3.1.
(a) f(6) = (6– 2) (8 – 6) = 4 · 2 = 8
f(- 1) is not defined since f(x) is defined only for 2
8.
(b) The set of all x such that 2 < x < 8.
(c) f(1 – 2t) = {(1 – 2t) – 2} {8 – (1 – 21)} = – (1 + 2t) (7 + 2t) where t is such that 2
- 7/2 <I<- 1/2.
1– 2t
'§ 8; i.e.,
f(x)
(d) f(3) = (3 – 2) (8 – 3) = 5, ƒ [ f(3)] = f(5) = (5 – 2)(8 – 5) = 9.
f(5) = 9 so that f [ f(5)] = f(9) is not defined.
(e) The following table shows f(x) for various values of x.
6
3
4
5
6.
7
8
2.5
7.5
f(x) 0
8.
9
8
5
2.75 2.75
2-
Plot points (2, 0), (3, 5), (4, 8), (5, 9), (6, 8), (7, 5), (8, 0),
(2.5, 2.75), (7.5, 2.75). These points are only a few of the infi-
nitely many points on the required graph shown in the adjoining
Figure 3.5. This set of points defines a curve which is part of a
parabola.
Figure 3.5
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