Question 319099
<pre><b>
{{{"g(x)"=sqrt(x-3)+2}}}

What's under a square root radical must be {{{"">=0}}}, so

{{{x-3>=0}}}

So the domain of g is {{{x>=3}}} or [3,{{{infinity}}})

Now we built 

{{{x-3>=0}}}

up to the right side of g(x)

Take positive square roots of both sides:

{{{sqrt(x-3)>=sqrt(0)}}}

{{{sqrt(x-3)>=0}}}

Add 2 to both sides:

{{{sqrt(x-3)+2>=2}}}

So the left side now equals g(x), so

{{{g(x)>=2}}}

So the range of g is [2,{{{infinity}}}).

{{{graph(400,400,-10,10,-10,10,sqrt ( x - 3 ) + 2)}}}.

Edwin</pre>