Math Help - help me solve this problem please..

1. help me solve this problem please..

f: R to R. For all open subset U of R, we have f(U) is open, too.

Prove that: f is monotonic.

2. Originally Posted by felixmcgrady
f: R to R. For all open subset U of R, we have f(U) is open, too.

Prove that: f is monotonic.
If $f$ is not monotonic, it will have a local extremum at some point $x_0$. What can you say about an open ball around $f(x_0)$?