Writing Inverse Functions to Solve Problems (Step Functions & Graph Symmetry)

This example demonstrates how to write an inverse function to solve problems by converting a forward function relationship into a reverse-solving task. It highlights the graphical idea that inverse pairs correspond to exchanged input-output roles, which is reflected visually by the structure of the function graph (especially for step functions). Key concepts include functions and inverse functions, inverse relationships, and how piecewise/step functions are represented on the coordinate plane. Construction-wise, the GeoGebra setup uses text1 and text2 for guiding the key steps and conclusions, and a set of points A1–A7 and B1–B7 to represent discrete input-output pairs. By pairing these points appropriately (swapping x and y roles), the diagram supports forming the algebraic inverse-writing strategy and connecting it to the symmetry/relationship between the original and inverse representations. Suitable for secondary school through early college, for instruction or practice on inverse functions and function graph interpretation.