How to Find the Inverse of a Linear Function Algebraically

Miacademy & MiaPrep Learning Channel

This concise mathematics tutorial guides students through the process of finding the inverse of linear functions algebraically. Building upon the concept of graphical inverses where coordinates are swapped, the video demonstrates how this same principle applies to algebraic equations by swapping variables x and y. The narrator provides a clear four-step framework: rewriting function notation as y, swapping variables, solving for y, and rewriting the result in inverse function notation. The video walks through three distinct examples of increasing complexity, including equations with fractions and negative slopes. It connects the algebraic result back to the conceptual understanding of inverses by verifying solutions through input/output mapping and graphical reflection across the line y = x. The lesson culminates in a "pause and try" opportunity for students to practice the skill independently before seeing the solution. This resource is highly valuable for Algebra 1 and Algebra 2 classrooms as it bridges procedural skills (solving for a variable) with conceptual depth (understanding inverses as reversing operations). Teachers can use this video to introduce the algebraic method after students have mastered the concept graphically, or as a review tool for students struggling with the multi-step process of isolating variables.