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 1.1 : Review : Functions
25. Find the domain of \(\displaystyle g\left( t \right) = \frac{{6t - {t^3}}}{{7 - t - 4{t^2}}}\).
Show SolutionIn this case we need to avoid division by zero issues so we’ll need to determine where the denominator is zero. To do this we will solve,
\[7 - t - 4{t^2} = 0\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}t = \frac{{1 \pm \sqrt {{{\left( { - 1} \right)}^2} - 4\left( { - 4} \right)\left( 7 \right)} }}{{2\left( { - 4} \right)}} = - \frac{1}{8}\left( {1 \pm \sqrt {113} } \right)\]The two values above are the only values of \(t\) that we can’t plug into the function. All other values of \(t\) can be plugged into the function and will return real values. The domain is then,
\[{\mbox{Domain : All real numbers except }}t = - \frac{1}{8}\left( {1 \pm \sqrt {113} } \right)\]