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

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- Mar 14th 2010, 05:45 PMzhupolongjoeinteresting question
is there a continuous real-valued function on R which takes all its values exactly twice?

- Mar 14th 2010, 06:34 PMSoroban
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: .$\displaystyle f(x) \:=\:x^2$

- Mar 14th 2010, 06:39 PMskeeter
- Mar 14th 2010, 06:54 PMDrexel28
There is none. Want to see a proof?

- Mar 14th 2010, 07:00 PMzhupolongjoe
If you've got time...or even just the idea of the proof.

- Mar 14th 2010, 07:11 PMDrexel28
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.