I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 12.5 : Functions of Several Variables
2. Find the domain of the following function.
\[f\left( {x,y} \right) = \ln \left( {2x - 3y + 1} \right)\] Show SolutionThere really isn’t all that much to this problem. We know that we can’t have negative numbers or zero in a logarithm so we’ll need to require that whatever \(\left( {x,y} \right)\) is it will need to satisfy,
\[2x - 3y + 1 > 0\]Since this is the only condition we need to meet this is also the domain of the function.
Let’s do a little rewriting on this so we can attempt to sketch the domain.
\[2x + 1 > 3y\hspace{0.5in}\Rightarrow \hspace{0.5in}y < \frac{2}{3}x + \frac{1}{3}\]So, it looks like we need to be below the line above. The domain is illustrated by the green area in the sketch below.
Note that we dashed the graph of the “bounding” line to illustrate that we don’t take points from the line itself.