Question

How do you find the domain and range of this function `f(x) = log_2(x-1) +3`?

Answer 1

The argument of the log-function may not be zero or negative.

So `x-1>0->x>1` so the domain is `1 < x < oo`

The range is unlimited. As `x->1` (from above) the log-function can go very negative, or:

`lim_(x->1^+)log_2 (x-1)+3=-oo`

On the other side, is `x` gets larger, so does the funtion:

`lim_(x->oo)log_2 (x-1)+3=oo`