If , is the commune of f(x) x>1? If this is what you mean then commune I take to mean domain of x. I fear though this is not exactly what you mean. Try looking around online for different vocabulary to use. I'm sorry I don't quite get you. Maybe someone else will and I'm missing something.
I attached the graph of the second expression.
As you can see, the y values covered are
I hope I understood you correctly. You may want to refer to these terms as domain ("beginning commune") and range ("end commune").
however, is the set for which the logarithm are greater than or equal to zero. This is the domain set for the expression. Note that