Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Question
Chapter 15.3, Problem 3E
To determine
The Fourier integral representation of the given function.
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In Problems 47–52, find functions f and g so that f ∘ g = H.
In Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x))
any values of x that need to be excluded.
= x. Give
27. f(x) = 3x + 4; g(x) =
(x- 4)
28. f(x) = 3 – 2x; g(x) = -(x – 3)
29. f(x) = 4x – 8; 8(x) = + 2
30. f(x) = 2x + 6; 8(x) = ;x - 3
31. f(x) = x' - 8; g(x)·
Vx + 8
32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2
33. f(x) = ; 8(x) =
34. f(x) = x; g(x)
x - 5
2x + 3'
2x + 3
4x - 3
3x + 5
35. f(x)
*: 8(x) =
8(x)
36. f(x) =
1- 2x
x + 4
2 - x
1.7
82 CHAPTER 1 Graphs and Functions
In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as
a hint), the graph of y = x is also given.
37.
y= X
38.
39.
y =X
3
(1, 2),
(0, 1)
(-1,0)
(2. )
(2, 1)
(1, 0) 3 X
(0, -1)
-3
(-1, -1)
3 X
-3
(-2, -2)
(-2, -2)
-하
-하
-하
40.
41.
y = x
42.
y = X
(-2, 1).
-3
3 X
(1, -1)
In Problems 23–30, use the given zero to find the remaining zeros of each function.
23. f(x) = x - 4x² + 4x – 16; zero: 2i
24. g(x) = x + 3x? + 25x + 75; zero: -5i
25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i
26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i
%3D
27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i
29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i
28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i
30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3i
Chapter 15 Solutions
Advanced Engineering Mathematics
Ch. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.1 - Prob. 6ECh. 15.1 - Prob. 8ECh. 15.1 - Prob. 11ECh. 15.1 - Prob. 12ECh. 15.1 - Prob. 13ECh. 15.1 - Prob. 14E
Ch. 15.1 - Prob. 15ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5ECh. 15.2 - Prob. 6ECh. 15.2 - Prob. 7ECh. 15.2 - Prob. 8ECh. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Prob. 20ECh. 15.2 - Prob. 21ECh. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.3 - Prob. 7ECh. 15.3 - Prob. 8ECh. 15.3 - Prob. 9ECh. 15.3 - Prob. 10ECh. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.4 - Prob. 7ECh. 15.4 - Prob. 8ECh. 15.4 - Prob. 9ECh. 15.4 - Prob. 10ECh. 15.4 - Prob. 11ECh. 15.4 - Prob. 12ECh. 15.4 - Prob. 13ECh. 15.4 - Prob. 14ECh. 15.4 - Prob. 15ECh. 15.4 - Prob. 16ECh. 15.4 - Prob. 17ECh. 15.4 - Prob. 18ECh. 15.4 - Prob. 19ECh. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - Prob. 28ECh. 15 - Prob. 1CRCh. 15 - Prob. 2CRCh. 15 - Prob. 3CRCh. 15 - Prob. 4CRCh. 15 - Prob. 5CRCh. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 15CRCh. 15 - Prob. 18CRCh. 15 - Prob. 19CRCh. 15 - Prob. 20CRCh. 15 - Prob. 21CR
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