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

Apr 14, 2015

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

So $x - 1 > 0 \to x > 1$ so the domain is $1 < x < \infty$

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

${\lim}_{x \to {1}^{+}} {\log}_{2} \left(x - 1\right) + 3 = - \infty$

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

${\lim}_{x \to \infty} {\log}_{2} \left(x - 1\right) + 3 = \infty$