Functional Equations Masterclass 1 | The Ultimate FE Toolkit | Setup, Substitutions & 40+ SE

Most students treat Functional Equations as random tricks. They're not. In this lecture you'll build the exact framework expert problem solvers use before attempting any Functional Equation. In this lecture: ✔ What Functional Equations really are ✔ The 3 Fundamental Questions to ask before solving any FE ✔ The complete Substitution Toolkit (7 essential substitutions) ✔ A systematic substitution ladder that works on most JEE problems ✔ Common mistakes and hidden traps ✔ 40+ carefully selected solved examples We start with the Three-Question Setup Check (domain, codomain, regularity) and see exactly why it matters: the same equation f(x+y) = f(x)+f(y) can have a unique solution, infinitely many solutions, or an uncountable wilderness of pathological ones — depending entirely on what's not stated. You'll see Cauchy's equation in all its disguises, understand why "continuous" appears in problem statements, and build the working vocabulary (injective, involution, idempotent, periodic, fixed point) you'll use for the rest of the series. Then we go into the Substitution Toolkit — seven ranked moves (plug zero, set y = x, set y = −x, swap x↔y, substitute an involution, feed f into itself, cash in regularity) that between them open up the vast majority of JEE Advanced, ISI UGA/UGB, and CMI FE problems, usually within the first thirty seconds of reading the question. Timestamps 00:00:00 — Functional equations & the 3 fundamental questions 00:06:58 — Prerequisites (domain, codomain, regularity, vocabulary) 00:21:12 — The Substitution Toolkit (40+ solved examples) Who this is for: JEE Advanced aspirants, ISI UGA/UGB and CMI entrance candidates, and anyone building serious olympiad-level FE technique from the ground up. Recurrance relation video link    • Sequence & Series | Lecture 9 | Recurrence...