Prove gof is Invertible & Find Its Inverse | Step-by-Step | BCS405A

Master composition and inverse of functions with an important VTU model question, explained step-by-step. Perfect for BCS405A students to understand invertibility of composite functions clearly. ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: ❓ Let A = B = C = R. Let f: A → B and g: B → C be defined by f(a) = 2a + 1 and g(b) = b / 3, for all a ∈ A, b ∈ B. Compute g ∘ f and show that g ∘ f is invertible. Find the inverse of g ∘ f. 📆 Asked in: • Model Question Paper 2 – Question 5(c) 📘 Subject: Discrete Mathematical Structures 📚 Subject Code: BCS405A 📌 Module 3 – Relations and Functions 📝 Topic: Composite Function Inverse ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: • Composition of functions (g ∘ f) • Simplifying composite expressions • Checking invertibility of functions • Finding inverse of linear functions • Solving VTU exam questions efficiently ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Continue This Topic (Equivalence Relation)    • Prove Reflexivity, Symmetry, Transitivity ...   2️⃣ Related Important Question (Composition Law Proof)    • h ∘ (g ∘ f) = (h ∘ g) ∘ f | The Proof That...   3️⃣ Full Playlist (Watch in Order)    • Relations and Functions | BCS405A Module 3...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): Relations and Functions | BCS405A Module 3    • Relations and Functions | BCS405A Module 3...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Topics: 1️⃣ Inverse Function Proof    • Prove g is Inverse of f | Step-by-Step Alg...   2️⃣ Composition with Parameters    • Find a & b When Given (g ∘ f)(x) | Composi...   3️⃣ Function Counting    • From A to B: Total Functions, Injective Fu...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Move to relations and equivalence relations. 📌 Don’t stop here: Practice composition and inverse together for strong concepts. ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ 📙 All BCS405A Playlists: ▶️ Module 1 – Fundamentals of Logic    • BCS405A Module 1 – Fundamentals of Logic |...   ▶️ Module 2 – Properties of Integers    • BCS405A Module 2( Discrete Mathematics )   ▶️ Module 3 – Relations and Functions    • Relations and Functions | BCS405A Module 3...   ▶️ Module 4 – Recurrence and Inclusion-Exclusion    • BCS405A Module 4  ( The principle of exclu...   ▶️ Module 5 – Group Theory    • BCS405A Module 5 (Group Theory)   ━━━━━━━━━━━━━━━━━━━━━ #DiscreteMathematics #BCS405A #FunctionComposition #InverseFunction #VTUMaths #EngineeringMaths #VTUExam