Can a Continuous Bijection Have a Discontinuous Inverse?

[To0ta]

find : E$$\subseteqR$$

f : E$$\rightarrowR$$

1_1 , onto , contonuo

such that

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

is not continows

Please help me in finding a solution

 

[Mentallic]

Can you repost it such that it's more readable please?

 

[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.

Is this your question?

 

[To0ta]

Yes, this is my question​

 

[Gregg]

what about e^x?

 

[Mark44]

Yes, this is my question​

Why don't you just type your question? All of the stuff you are doing with special fonts, centering, and font size is distracting.