In MUX single input line is enough to generate different kind of output signal. Because different kind of output depend on select line, not on input line
See for 3 variable, we can just 1 as input line, 2 as select line
if Say X is input line, and A,B are select line
then outputs are A'B'X+A'BX+AB'X+ABX
So, output variation depend on only select line , not input line .confirmed!!
But here NOT gate actually not doing any huge difference.
It only giving some input as NOT signal.
So, without NOT gate, without NOT gate, with buffer any case we get $2^{n-1}$ line to 1 line
I think same case going to happen with AND, OR............with any gate also