# interesting question

• March 14th 2010, 05:45 PM
zhupolongjoe
interesting question
is there a continuous real-valued function on R which takes all its values exactly twice?
• March 14th 2010, 06:34 PM
Soroban
Hello, zhupolongjoe!

I hope I didn't misread the problem . . .

Quote:

Is there a continuous real-valued function on R
which takes all its values exactly twice?

How about: . $f(x) \:=\:x^2$

• March 14th 2010, 06:39 PM
skeeter
Quote:

Originally Posted by Soroban
Hello, zhupolongjoe!

I hope I didn't misread the problem . . .

How about: . $f(x) \:=\:x^2$

problem is ... f(x) = 0 only once
• March 14th 2010, 06:54 PM
Drexel28
There is none. Want to see a proof?
• March 14th 2010, 07:00 PM
zhupolongjoe
If you've got time...or even just the idea of the proof.
• March 14th 2010, 07:11 PM
Drexel28
Quote:

Originally Posted by zhupolongjoe
If you've got time...or even just the idea of the proof.

Here is a similar proof. See if you can understand it, and if you can see if you can generalize to your question. If you have any trouble report back.

You may need to scroll down a little.