f(x) = log2(x – 3) + 1. How do I find the Domain and Range?

Answer 1

you know that log(u) has domain (0,∞) and range (-∞,+∞)

So, log(x-3) has domain (x-3)>0 or x>3.
That is (3,∞)

range is still the same. Adding 1 to ∞ makes no difference.