Domain of algebraic combination of functions for JEE

Formula

\[\begin{aligned}D(f\pm g)&=D(f)\cap D(g),\\ D(fg)&=D(f)\cap D(g),\\ D\!\left(\frac{f}{g}\right)&=\{x\in D(f)\cap D(g):g(x)\neq 0\}\end{aligned}\]

Variables: \(D(f)\) denotes domain of function \(f\).

Conditions: Applicable for real-valued functions where the operations are defined.

Finding domain of combined functions and checking validity before limits/continuity/differentiation.