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 1.2 : Inverse Functions
4. Find the inverse for \(g\left( x \right) = 4{\left( {x - 3} \right)^5} + 21\). Verify your inverse by computing one or both of the composition as discussed in this section.
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Finally, compute either \(\left( {g \circ {g^{ - 1}}} \right)\left( x \right)\) or \(\left( {{g^{ - 1}} \circ g} \right)\left( x \right)\) to verify our work.
Show Step 4Either composition can be done so let’s do \(\left( {g \circ {g^{ - 1}}} \right)\left( x \right)\) in this case.
\[\begin{align*}\left( {g \circ {g^{ - 1}}} \right)\left( x \right) & = g\left[ {{g^{ - 1}}\left( x \right)} \right]\\ & = 4{\left( {\left[ {3 + \sqrt[5]{{\frac{1}{4}\left( {x - 21} \right)}}} \right] - 3} \right)^5} + 21\\ & = 4{\left( {\sqrt[5]{{\frac{1}{4}\left( {x - 21} \right)}}} \right)^5} + 21\\ & = 4\left( {\frac{1}{4}\left( {x - 21} \right)} \right) + 21\\ & = \left( {x - 21} \right) + 21\\ & = x\end{align*}\]So, we got \(x\) out of the composition and so we know we’ve done our work correctly.