|Jul24-07, 03:29 AM||#1|
Absolute Values and Continuous Functions
1. The problem statement, all variables and given/known data
We recently proved that if a function, f, is continuous, it's absolute value |f| is also continuous. I know, intuitively, that the reverse is not true, but I'm unable to come up with an example showing that, |f| is continuous, b f is not. Any examples or suggestions would be appreciated. Thanks!
2. Relevant equations
3. The attempt at a solution
|Jul24-07, 04:29 AM||#2|
Blog Entries: 5
What about [itex]f(x) = -1[/itex] if [itex]x < 0[/itex] and 1 if [itex]x \ge 0[/itex]?
Then [itex]|f(x)| = 1[/itex] for all x - about as continuous as you get them, but f is not. In fact, you could even do something pathetic like make f equal -1 on all rationals and 1 on all irrational numbers :)
|Similar Threads for: Absolute Values and Continuous Functions|
|Continuous function from Continuous functions to R||Calculus & Beyond Homework||2|
|Absolute Values||Precalculus Mathematics Homework||5|
|Help On Absolute Values||Introductory Physics Homework||3|
|Absolute values||Introductory Physics Homework||12|
|Blackjack with continuous card values||General Math||0|