The main results are: Firstly, for any two surjections, $\text{f}$ and $\text{g}$, of a real interval there exist connected surjections $\mathrm{\alpha }$ and $\mathrm{\beta }$ such that a $\mathrm{\alpha }(\text{f}(\text{x}))=\text{g}(\mathrm{\beta }(\text{x}))$ for all $\text{x}$. Secondly, there exists a pair of connected functions whose composition is not connected, mod the continuum hypothesis.