The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Restricting a quadratic to obtain an inverse
Use a vertex to choose a maximal one-one branch.
Select the correct square-root sign.
Transfer strict or finite endpoint restrictions to the inverse.
A quadratic is one-one on either side of its vertex, but not across it. Choose the square-root sign from the ORIGINAL domain. An inverse function has one output, so do not leave \(\pm\) in its rule. A restricted endpoint need not be the vertex.