Inverse function criterion for JEE

Formula

\[f^{-1}(f(x))=x\ (x\in D(f)),\qquad f(f^{-1}(y))=y\ (y\in R(f))\]

Variables: \(D(f)\) and \(R(f)\) denote domain and range.

Conditions: Inverse exists when \(f\) is one-one and onto its range.

Finding inverse, composition, derivative of inverse, solving equations.