How to Find the Inverse of a Rational Function

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step guide on how to find the inverse of a rational function. Hosted by an instructor named Randy, the lesson begins by defining what an inverse function is conceptually—specifically, the swapping of x and y coordinates. It outlines a systematic three-step process for finding inverses algebraically: replacing function notation with 'y', switching 'x' and 'y' variables, and solving for the new 'y'. The video uses a specific example of a rational function to demonstrate these steps in real-time. The core of the video focuses on the algebraic manipulation required to solve for 'y' when it appears in both the numerator and denominator of a rational equation. This involves skills such as cross-multiplication, the distributive property, grouping variable terms on one side of the equation, and factoring. The narrator emphasizes common stumbling blocks, particularly the crucial step of factoring out 'y' to isolate the variable. The video concludes by connecting the algebraic result to a graphical representation, showing how the graphs of a function and its inverse are related through reflection. For educators, this video serves as an excellent instructional tool for Algebra II or Pre-Calculus units on functions. It addresses a specific skill gap—handling rational functions where the variable to be isolated appears twice—which is often challenging for students. The clear visual aids, explicit written steps, and side-by-side graphical comparison make it suitable for direct instruction, flipped classroom assignments, or as a review resource for students struggling with algebraic manipulation of complex functions.