Ok, so I would like to know how to prove the following proof. If anyone has any insight I would greatly appreciate it.

Suppose is pathwise connected and \rightarrow R" alt="f\rightarrow R" /> is continuous. Prove that is an interval.

Is it enough to create a function that is continuous and then show that the function lives on an interval?

For example, where and . Then show that the function lives on the interval [0,1]?