69. Draw graphs of each of these functions. a) f(x) = [x+] c) f(x) = [x/3] e) f(x) = [x-21 + (x+2) ir JA1 b) f(x)= [2x+1] d) f(x) = [1/x]
69. Draw graphs of each of these functions. a) f(x) = [x+] c) f(x) = [x/3] e) f(x) = [x-21 + (x+2) ir JA1 b) f(x)= [2x+1] d) f(x) = [1/x]
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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Can anyone please help me with question 69 e please? I’m stuck on it
![R to R.
69. Draw graphs of each of these functions.
a) f(x) = (x + ]
b) f(x) = (2x + 1]
d) f(x) = [1/x]
c) f(x) = [x/31
e) f(x)=[x-21+x+2)
f) f(x)= [2x][x/2]
from
g) f(x) = [[x - 1 + 1
70. Draw graphs of each of these functions.
a) f(x) = [3x-2]
c) f(x): [-1/x]
e) f(x) = [x/2] [x/2]
g) f(x)= [2 [x/21 + 1
b) f(x) = [0.2x]
d) f(x) = [x²]
f) f(x) = [x/2] + [x/2]
71. Find the inverse function of f(x) = x³ + 1.
72. Suppose that f is an invertible function from Y to Z and
g is an invertible function from X to Y. Show that the
inverse of the composition fog is given by (fog)-¹ =
73. Let S be a subset of a universal set U. The character-
istic function fs of S is the function from U to the set
(0, 1) such that f(x) = 1 if x belongs to S and f(x) = 0
if x does not belong to S. Let A and B be sets. Show that
for all x EU,
80. a) SP
as
ele
b) Us
res
81. a) She
pos
der
b) Sho
me
one
*82. Show t
subset
dence b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2Fcba0a192-991c-4165-bce3-39202e55dc1d%2Fa6il2f9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:R to R.
69. Draw graphs of each of these functions.
a) f(x) = (x + ]
b) f(x) = (2x + 1]
d) f(x) = [1/x]
c) f(x) = [x/31
e) f(x)=[x-21+x+2)
f) f(x)= [2x][x/2]
from
g) f(x) = [[x - 1 + 1
70. Draw graphs of each of these functions.
a) f(x) = [3x-2]
c) f(x): [-1/x]
e) f(x) = [x/2] [x/2]
g) f(x)= [2 [x/21 + 1
b) f(x) = [0.2x]
d) f(x) = [x²]
f) f(x) = [x/2] + [x/2]
71. Find the inverse function of f(x) = x³ + 1.
72. Suppose that f is an invertible function from Y to Z and
g is an invertible function from X to Y. Show that the
inverse of the composition fog is given by (fog)-¹ =
73. Let S be a subset of a universal set U. The character-
istic function fs of S is the function from U to the set
(0, 1) such that f(x) = 1 if x belongs to S and f(x) = 0
if x does not belong to S. Let A and B be sets. Show that
for all x EU,
80. a) SP
as
ele
b) Us
res
81. a) She
pos
der
b) Sho
me
one
*82. Show t
subset
dence b
![67. Draw the graph of the function f(x) = [x] + [x/2] from
R to R.
68. Draw the graph of the function f(x) = [x] + [x/2] from
R to R.
69. Draw graphs of each of these functions.
a) f(x) = [x+ -]
b) f(x) = (2x + 1]
d) f(x) = [1/x]
c) f(x) = [x/3]
e) f(x) = [x-21] + [x+2]
f) f(x) = [2x] [x/2]
x/21 [x/2]
g) f(x) = [[x] + 1
70. Draw graphs of each of these functions.
a) f(x) = [3x-2]
-1/x]
c) f(x) =
e) f(x) =
g) f(x) = [2 [x/2] + J
b) f(x) = [0.2x]
d) f(x) = [x²]
f) f(x) = [x/2] + [x/2]
71. Find the inverse function of f(x) = x²³ +1.
72. Suppose that f is an invertible function from Y to Z and
g is an invertible function from X to Y. Show that the
inverse of the composition fog is given by (fog)-¹ =
g-¹ of ¹.
73. Let S be a subset of a universal set II The character.
80.
E
81. a
b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2Fcba0a192-991c-4165-bce3-39202e55dc1d%2F9wmf39j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:67. Draw the graph of the function f(x) = [x] + [x/2] from
R to R.
68. Draw the graph of the function f(x) = [x] + [x/2] from
R to R.
69. Draw graphs of each of these functions.
a) f(x) = [x+ -]
b) f(x) = (2x + 1]
d) f(x) = [1/x]
c) f(x) = [x/3]
e) f(x) = [x-21] + [x+2]
f) f(x) = [2x] [x/2]
x/21 [x/2]
g) f(x) = [[x] + 1
70. Draw graphs of each of these functions.
a) f(x) = [3x-2]
-1/x]
c) f(x) =
e) f(x) =
g) f(x) = [2 [x/2] + J
b) f(x) = [0.2x]
d) f(x) = [x²]
f) f(x) = [x/2] + [x/2]
71. Find the inverse function of f(x) = x²³ +1.
72. Suppose that f is an invertible function from Y to Z and
g is an invertible function from X to Y. Show that the
inverse of the composition fog is given by (fog)-¹ =
g-¹ of ¹.
73. Let S be a subset of a universal set II The character.
80.
E
81. a
b
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