# Combining functions - is this a case for Piecewise?

I have a function $Eb1$ which was the subject of a question I asked recently - you can see it here on stack exchange. Now, in that example it's specified between a boundary $r_n$ and $r_o$ where $r_o > r_n$ and it works as expected. I also want to specify the value of the function between 0 and $r_n$ - fcor all $r < r_n$, the function is a constant with the value $Eb1(r_n)$, so the same value it is at the boundary. I am however unsure how to code this, and how to combine these two specifications into a single expression.

I was considering using piece-wise, but I am unclear about how to specify this and so far my attempts have failed. Any ideas?

Ebound[r_] =