Question 11: Let f(x) = |- x +7|-|-3+x|, where r E R. Let Z = {x: f(x) > 0} . Give explicitly the fully simplified expression for Z.
Question 11: Let f(x) = |- x +7|-|-3+x|, where r E R. Let Z = {x: f(x) > 0} . Give explicitly the fully simplified expression for Z.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
Related questions
Question
100%
![Question 11:
Let f(x) =|– x+7| – |- 3+x|, where x E R. Let Z = {x: f(x) > 0} .
Give explicitly the fully simplified expression for Z.
Question 12:
[ 3r
Зх — 2,
if x < k
Let k e R be a parameter and set fk(æ)=
-2x + 3, otherwise.
Give an explicit expression for T = {k € R: ƒk is continuous on R} .
Question 13:
Let a = 2m + 1, m e N and k E R. Set
P = {r € R: |2x – 1| > a} and
-
Q = {x € R: |x + k| < 3} .
(a) Give explicitly P an Q.
(b) Assuming m+ k < 2 and m – k < 3, give PnQ.
Question 14:
Let G = {-1,3,7}UV, where V = [(-3, 1] U [2, 5)] N (-2, 4).
Let H = {x € R: G is a neighborhood of x}. That is H is the set of all
real numbers admitting G as neighborhood.
Give a simplified expression for both G and H.
Question 15:
Suppose that the function f (x) is continuous at a e R and (xn) is a se-
quence in dom(f) that converges to a. Let w(x)
sin([f(x)]²)e*
cos(r)+2
Give lim,,→∞ w(xn).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a44e4ff-1ba1-406c-801b-9669a60ff7fb%2F47708681-41ee-4231-938d-1e059f388e55%2Fjwydbzd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 11:
Let f(x) =|– x+7| – |- 3+x|, where x E R. Let Z = {x: f(x) > 0} .
Give explicitly the fully simplified expression for Z.
Question 12:
[ 3r
Зх — 2,
if x < k
Let k e R be a parameter and set fk(æ)=
-2x + 3, otherwise.
Give an explicit expression for T = {k € R: ƒk is continuous on R} .
Question 13:
Let a = 2m + 1, m e N and k E R. Set
P = {r € R: |2x – 1| > a} and
-
Q = {x € R: |x + k| < 3} .
(a) Give explicitly P an Q.
(b) Assuming m+ k < 2 and m – k < 3, give PnQ.
Question 14:
Let G = {-1,3,7}UV, where V = [(-3, 1] U [2, 5)] N (-2, 4).
Let H = {x € R: G is a neighborhood of x}. That is H is the set of all
real numbers admitting G as neighborhood.
Give a simplified expression for both G and H.
Question 15:
Suppose that the function f (x) is continuous at a e R and (xn) is a se-
quence in dom(f) that converges to a. Let w(x)
sin([f(x)]²)e*
cos(r)+2
Give lim,,→∞ w(xn).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage