Let functions $f_{1}:I_{1} \rightarrow \mathbb R$ $f_{2}:I_{2} \rightarrow I_{1}$ where $I_{i}=(a,b)$ for $i=1,2$ $a,b \in \mathbb R$.
If $f_{1}, f_{2}$ are convex then $f \circ g$ is also convex.
I think this implication is not truth so I'm looking for a counter-example for her.
However I have been doing this job for a long time and I have not been able to find anything.
Have you any ideas?
