# Math Help - interesting question

1. ## interesting question

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

2. Hello, zhupolongjoe!

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

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

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

3. 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

4. There is none. Want to see a proof?

5. If you've got time...or even just the idea of the proof.

6. 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.