Let the function f : D → R be continuous. Then define the function |f| : D → R by \S\(x) = \f(x)| for æ in D. Prove that |f|: D → R is continuous. (Hint: You can use the fact that if {a,} converges to a, then {|a,|} converges to |a|.) %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Let the function f : D → R be continuous. Then define the function [f| : D → R by
\F(x) = \f(x)| for x in D. Prove that |f| : D → R is continuous. (Hint: You can use the fact that if {a,} converges
to a, then {|an|} converges to |a|.)
Transcribed Image Text:Let the function f : D → R be continuous. Then define the function [f| : D → R by \F(x) = \f(x)| for x in D. Prove that |f| : D → R is continuous. (Hint: You can use the fact that if {a,} converges to a, then {|an|} converges to |a|.)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,