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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
\[f^{-1}(f(x)) = x\]