How to reverse the logic of rational functions
In short: This video explains how to find the inverse of a rational function by treating it as a mapping problem. It demonstrates the algebraic process of swapping inputs and outputs to undo an operation.
The core concept involves understanding that an inverse function maps every output in a function's range back to its corresponding input in the domain. To find this expression algebraically, you solve the equation x = f(y) for the variable y.
By following this method with rational functions—which are ratios of polynomials—you can systematically isolate the original input. This process is a fundamental component of Algebra 2, helping students understand how to 'undo' mathematical operations.
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Sources
- Summary by Intellect · source: Finding inverses of rational functions | Equations | Algebra 2 | Khan Academy
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