Composition of functions and domain for JEE

Formula

\[D(f\circ g)=\{x\in D(g):g(x)\in D(f)\},\qquad (f\circ g)(x)=f(g(x))\]

Variables: \(f\circ g\) is composition of \(f\) and \(g\).

Conditions: Defined only when output of \(g\) lies in domain of \(f\).

Composite functions, chain rule, inverse functions, domain/range questions.