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

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Answer 1 · 2015-04-14T10:46:23

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:

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

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