AcademyFunctions
Academy
Inverse Functions
Level 1 - Math I (Physics) topic page in Functions.
Inverse Functions
An inverse function \(f^{-1} reverses the mapping of a function \)f. If \(f\) maps \(x\) to \(y\), then \(f^{-1}\) maps \(y\) back to \(x\).
Inverse Definition
\[f^{-1}(y) = x \Leftrightarrow f(x) = y\]
Horizontal Line Test
A function has an inverse only if it is one-to-one.
Fundamental Property
Inverse Composition
\[f^{-1}(f(x)) = x\]