If |f| is cts, is f?

[ahorn]

If |f| is continuous, where f is a function, does it imply that f is continuous?

 

[mmm4444bot]

If |f| is continuous, where f is a function, does it imply that f is continuous?

Hi ahorn:

This is a tutoring website; please try to include some of your own thoughts, when posting exercises. Volunteer tutors need some idea of why you're stuck.

For example, we do not know whether you've yet learned the meaning of continuity. We don't know whether you've worked with (or seen) absolute-value graphs of functions before.

What have you tried or thought about, thus far? Please show some effort.

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Thank you! :cool:

 

[Quaid]

If |f| is cts, is f?

If |f| is continuous, where f is a function, does it imply that f is continuous?

Did your fingers hurt, while typing your subject line, or did you get cts from your teacher?

CTS is an acronym for Carpal Tunnel Syndrome; it also represents a vehicle model from Cadillac (Catera Touring Sedan); CTS pertains to a class of genes (see 'cathepsins'); it's a university, a spacecraft, a title, a unit for count. But cts is not a symbol for the word 'continuous', unless you define it as such before using it!

---

Here's a hint.

Look up "jump discontinuity", and then consider the graph of |f| when f is a piecewise function containing a jump discontinuity. Try sketching such scenarios, and see whether you can come up with a continuous |f| from a discontinous f.

Ciao

 

[pka]

If |f| is continuous, where f is a function, does it imply that f is continuous?

Think about \(\displaystyle f(x) = \left\{ {\begin{array}{*{20}{rl}}{1,}&{x \ge 0}\\
{ - 1,}&{x < 0}
\end{array}} \right.\)

 

[mmm4444bot]

Try sketching such scenarios, and see whether you can come up with a continuous |f| from a discontinous f.

Or, just wait for somebody to give you one? :?

 

[HallsofIvy]

Now, can you come up with a function, f, such that |f| is continuous but f is discontinuous at every number?

 

[ahorn]

Now, can you come up with a function, f, such that |f| is continuous but f is discontinuous at every number?

\(\displaystyle f(x) = \left\{ \begin{array}{1,1}1, & \quad x \in Q\\
-1, & \quad else
\end{array} \right. \)

?