Class 12 Math: Relations and Functions Quick Revision Chapter Summary
Need to review the entire chapter before a test? This quick revision guide summarizes all the core concepts, topics, and equations taught in Class 12 Relations and Functions to help you refresh your memory instantly.
Core Topics At a Glance
### 📌 Types of relations (reflexive, symmetric, transitive, equivalence) Relations describe connections. A relation on set A is Reflexive if every element relates to itself; Symmetric if aRb implies bRa; Transitive if aRb and bRc implies aRc. An Equivalence relation satisfies all three properties.
### 📌 One-to-one and onto functions (injective, surjective, bijective) An Injective function maps distinct inputs to distinct outputs. A Surjective function maps onto the entire codomain (Range = Codomain). A Bijective function is both injective and surjective.
### 📌 Composite functions A composite function is a function formed by applying one function to the output of another. The composite function g ∘ f is defined as g(f(x)).
### 📌 Inverse of a function The inverse of a function f maps outputs back to their original inputs. A function has a unique inverse function f⁻¹ if and only if it is bijective.
Key Formulas Mind Map
- Composition of Functions: `(g \circ f)(x) = g(f(x))` - Evaluates function g on the output of function f....
Revision Checklist
- Review the subtopic guides and outline notes.
- Practice writing the key formulas from memory.
- Solve at least 3 worked examples and check your steps.
- Take a timed practice quiz to verify your speed.