The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
A function and its inverse on a graph
Reflect complete graph features in y=x.
Preserve open endpoints, domains and ranges.
Find common points with justification; recognise decreasing counterexamples.
Reflection in \(y=x\) sends \((u,v)\) to \((v,u)\). Mark the mirror line on sketches and preserve open or closed endpoints. For a strictly increasing function, common points with its inverse are fixed points. This need not hold for a decreasing function.