Answer:
The domain is [tex]x>1[/tex] (or [tex]x\in (1,\infty)[/tex]), the range is whole real number line (or [tex]y\in(-\infty,\infty)[/tex]).
Step-by-step explanation:
Consider parent function [tex]y=\log_2x.[/tex] The domain of this function is [tex]x>0[/tex] (or [tex]x\in(0,\infty)[/tex]) and the range of this function is whole real number line (or [tex]y\in(-\infty,\infty)[/tex]).
The function [tex]g(x)=3\log_2(x-1)+4[/tex] can be obtained from the function [tex]y=\log_2x[/tex] by stretch with factor 3 and translation 1 unit to the right and 4 units up. Then the domain of this function becomes [tex]x>1[/tex] (or [tex]x\in (1,\infty)[/tex]) and the range doesn't change.
