Consider the function: { x > 0 f(x) = %3D x +3 x < 0 a. Use a 8, e argument to prove that f(x) is discontinuous at x = 0. b. Find an open set U C R such that f-1(U) is not open and hence f(x) is not continuous on R.
Consider the function: { x > 0 f(x) = %3D x +3 x < 0 a. Use a 8, e argument to prove that f(x) is discontinuous at x = 0. b. Find an open set U C R such that f-1(U) is not open and hence f(x) is not continuous on R.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 50HP
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Class: Mathematical Analysis/
![Consider the function:
{
x > 0
x + 3 x < 0
f(x) =
a. Use a d, e argument to prove that f(x) is discontinuous at x = 0.
b. Find an open set U CR such that f-1(U) is not open and hence f(x)
is not continuous on R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaa9c753-6b68-41b4-8837-61aa8aa0a19b%2Fb0e41481-ec08-400e-98fd-42a77231ebe5%2Fvqo7c2t_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function:
{
x > 0
x + 3 x < 0
f(x) =
a. Use a d, e argument to prove that f(x) is discontinuous at x = 0.
b. Find an open set U CR such that f-1(U) is not open and hence f(x)
is not continuous on R.
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