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
6. Find the inverse for \(f\left( x \right) = \sqrt[7]{{5x + 8}}\). Verify your inverse by computing one or both of the composition as discussed in this section.
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Finally, compute either \(\left( {f \circ {f^{ - 1}}} \right)\left( x \right)\) or \(\left( {{f^{ - 1}} \circ f} \right)\left( x \right)\) to verify our work.
Show Step 4Either composition can be done so let’s do \(\left( {f \circ {f^{ - 1}}} \right)\left( x \right)\) in this case.
\[\begin{align*}\left( {f \circ {f^{ - 1}}} \right)\left( x \right) & = f\left[ {{f^{ - 1}}\left( x \right)} \right]\\ & = \sqrt[7]{{5\left[ {\frac{1}{5}\left( {{x^7} - 8} \right)} \right] + 8}}\\ & = \sqrt[7]{{\left[ {{x^7} - 8} \right] + 8}}\\ & = \sqrt[7]{{{x^7}}}\\ & = x\end{align*}\]So, we got \(x\) out of the composition and so we know we’ve done our work correctly.