How to Find, Verify, and Graph Inverse Functions

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on inverse functions, a core concept in high school algebra and pre-calculus. The video begins by demonstrating the algebraic method for finding an inverse: replacing f(x) with y, switching x and y, and solving for the new y. It walks through several examples of increasing complexity, including linear, quadratic, and radical functions. The content expands beyond simple calculation to include verification methods using function composition, showing that f(g(x)) must equal x for functions to be inverses. The video also explores the graphical relationship between a function and its inverse, illustrating how they are reflections across the line y=x. Finally, it introduces the Horizontal Line Test as a tool to determine if a function's inverse will itself be a function, discussing concepts like one-to-one functions and domain restrictions. For educators, this video serves as an excellent primary resource for introducing or reviewing inverse functions. It addresses both procedural fluency (calculating inverses) and conceptual understanding (graphical symmetry and function definition). The visual explanations of why some inverses are not functions (like the full parabola) are particularly useful for clarifying common student misconceptions about domains and ranges.