1. Apr 6, 2010

### To0ta

find : E$$\subseteqR$$

f : E$$\rightarrowR$$

1_1 , onto , contonuo

such that

f$$^{}-1$$ : f(E) $$\rightarrowR$$

is not continows

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 6, 2010

3. Apr 6, 2010

### rs1n

Perhaps you meant:

Let $E\subseteq \mathbb{R}$. Find a function $f : E\rightarrow \mathbb{R}$ that is one-to-one, onto, and continuous such that $f^{-1} : f(E) \rightarrow \mathbb{R}$ is not continuous.

4. Apr 6, 2010

### To0ta

Yes, this is my question

5. Apr 6, 2010